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Chapter 3 Solving Problems by Searching 

When the correct action to take is not immediately obvious, an agent may need to plan ahead : to consider a sequence of actions that form a path to a goal state. Such an agent is called a problem-solving agent , and the computational process it undertakes is called search .

Problem-solving agents use atomic representations, that is, states of the world are considered as wholes, with no internal structure visible to the problem-solving algorithms. Agents that use factored or structured representations of states are called planning agents .

We distinguish between informed algorithms, in which the agent can estimate how far it is from the goal, and uninformed algorithms, where no such estimate is available.

3.1 Problem-Solving Agents 

If the agent has no additional information—that is, if the environment is unknown —then the agent can do no better than to execute one of the actions at random. For now, we assume that our agents always have access to information about the world. With that information, the agent can follow this four-phase problem-solving process:

GOAL FORMULATION : Goals organize behavior by limiting the objectives and hence the actions to be considered.

PROBLEM FORMULATION : The agent devises a description of the states and actions necessary to reach the goal—an abstract model of the relevant part of the world.

SEARCH : Before taking any action in the real world, the agent simulates sequences of actions in its model, searching until it finds a sequence of actions that reaches the goal. Such a sequence is called a solution .

EXECUTION : The agent can now execute the actions in the solution, one at a time.

It is an important property that in a fully observable, deterministic, known environment, the solution to any problem is a fixed sequence of actions . The open-loop system means that ignoring the percepts breaks the loop between agent and environment. If there is a chance that the model is incorrect, or the environment is nondeterministic, then the agent would be safer using a closed-loop approach that monitors the percepts.

In partially observable or nondeterministic environments, a solution would be a branching strategy that recommends different future actions depending on what percepts arrive.

3.1.1 Search problems and solutions 

A search problem can be defined formally as follows:

A set of possible states that the environment can be in. We call this the state space .

The initial state that the agent starts in.

A set of one or more goal states . We can account for all three of these possibilities by specifying an \(Is\-Goal\) method for a problem.

The actions available to the agent. Given a state \(s\) , \(Actions(s)\) returns a finite set of actions that can be executed in \(s\) . We say that each of these actions is applicable in \(s\) .

A transition model , which describes what each action does. \(Result(s,a)\) returns the state that results from doing action \(a\) in state \(s\) .

An action cost function , denote by \(Action\-Cost(s,a,s\pr)\) when we are programming or \(c(s,a,s\pr)\) when we are doing math, that gives the numeric cost of applying action \(a\) in state \(s\) to reach state \(s\pr\) .

A sequence of actions forms a path , and a solution is a path from the initial state to a goal state. We assume that action costs are additive; that is, the total cost of a path is the sum of the individual action costs. An optimal solution has the lowest path cost among all solutions.

The state space can be represented as a graph in which the vertices are states and the directed edges between them are actions.

3.1.2 Formulating problems 

The process of removing detail from a representation is called abstraction . The abstraction is valid if we can elaborate any abstract solution into a solution in the more detailed world. The abstraction is useful if carrying out each of the actions in the solution is easier than the original problem.

3.2 Example Problems 

A standardized problem is intended to illustrate or exercise various problem-solving methods. It can be given a concise, exact description and hence is suitable as a benchmark for researchers to compare the performance of algorithms. A real-world problem , such as robot navigation, is one whose solutions people actually use, and whose formulation is idiosyncratic, not standardized, because, for example, each robot has different sensors that produce different data.

3.2.1 Standardized problems 

A grid world problem is a two-dimensional rectangular array of square cells in which agents can move from cell to cell.

Vacuum world

Sokoban puzzle

Sliding-tile puzzle

3.2.2 Real-world problems 

Route-finding problem

Touring problems

Trveling salesperson problem (TSP)

VLSI layout problem

Robot navigation

Automatic assembly sequencing

3.3 Search Algorithms 

A search algorithm takes a search problem as input and returns a solution, or an indication of failure. We consider algorithms that superimpose a search tree over the state-space graph, forming various paths from the initial state, trying to find a path that reaches a goal state. Each node in the search tree corresponds to a state in the state space and the edges in the search tree correspond to actions. The root of the tree corresponds to the initial state of the problem.

The state space describes the (possibly infinite) set of states in the world, and the actions that allow transitions from one state to another. The search tree describes paths between these states, reaching towards the goal. The search tree may have multiple paths to (and thus multiple nodes for) any given state, but each node in the tree has a unique path back to the root (as in all trees).

The frontier separates two regions of the state-space graph: an interior region where every state has been expanded, and an exterior region of states that have not yet been reached.

3.3.1 Best-first search 

In best-first search we choose a node, \(n\) , with minimum value of some evaluation function , \(f(n)\) .

3.3.2 Search data structures 

A node in the tree is represented by a data structure with four components

\(node.State\) : the state to which the node corresponds;

\(node.Parent\) : the node in the tree that generated this node;

\(node.Action\) : the action that was applied to the parent’s state to generate this node;

\(node.Path\-Cost\) : the total cost of the path from the initial state to this node. In mathematical formulas, we use \(g(node)\) as a synonym for \(Path\-Cost\) .

Following the \(PARENT\) pointers back from a node allows us to recover the states and actions along the path to that node. Doing this from a goal node gives us the solution.

We need a data structure to store the frontier . The appropriate choice is a queue of some kind, because the operations on a frontier are:

\(Is\-Empty(frontier)\) returns true only if there are no nodes in the frontier.

\(Pop(frontier)\) removes the top node from the frontier and returns it.

\(Top(frontier)\) returns (but does not remove) the top node of the frontier.

\(Add(node, frontier)\) inserts node into its proper place in the queue.

Three kinds of queues are used in search algorithms:

A priority queue first pops the node with the minimum cost according to some evaluation function, \(f\) . It is used in best-first search.

A FIFO queue or first-in-first-out queue first pops the node that was added to the queue first; we shall see it is used in breadth-first search.

A LIFO queue or last-in-first-out queue (also known as a stack ) pops first the most recently added node; we shall see it is used in depth-first search.

3.3.3 Redundant paths 

A cycle is a special case of a redundant path .

As the saying goes, algorithms that cannot remember the past are doomed to repeat it . There are three approaches to this issue.

First, we can remember all previously reached states (as best-first search does), allowing us to detect all redundant paths, and keep only the best path to each state.

Second, we can not worry about repeating the past. We call a search algorithm a graph search if it checks for redundant paths and a tree-like search if it does not check.

Third, we can compromise and check for cycles, but not for redundant paths in general.

3.3.4 Measuring problem-solving performance 

COMPLETENESS : Is the algorithm guaranteed to find a solution when there is one, and to correctly report failure when there is not?

COST OPTIMALITY : Does it find a solution with the lowest path cost of all solutions?

TIME COMPLEXITY : How long does it take to find a solution?

SPACE COMPLEXITY : How much memory is needed to perform the search?

To be complete, a search algorithm must be systematic in the way it explores an infinite state space, making sure it can eventually reach any state that is connected to the initial state.

In theoretical computer science, the typical measure of time and space complexity is the size of the state-space graph, \(|V|+|E|\) , where \(|V|\) is the number of vertices (state nodes) of the graph and \(|E|\) is the number of edges (distinct state/action pairs). For an implicit state space, complexity can be measured in terms of \(d\) , the depth or number of actions in an optimal solution; \(m\) , the maximum number of actions in any path; and \(b\) , the branching factor or number of successors of a node that need to be considered.

3.4 Uninformed Search Strategies 

3.4.1 breadth-first search .

When all actions have the same cost, an appropriate strategy is breadth-first search , in which the root node is expanded first, then all the successors of the root node are expanded next, then their successors, and so on.

Breadth-first search always finds a solution with a minimal number of actions, because when it is generating nodes at depth \(d\) , it has already generated all the nodes at depth \(d-1\) , so if one of them were a solution, it would have been found.

All the nodes remain in memory, so both time and space complexity are \(O(b^d)\) . The memory requirements are a bigger problem for breadth-first search than the execution time . In general, exponential-complexity search problems cannot be solved by uninformed search for any but the smallest instances .

3.4.2 Dijkstra’s algorithm or uniform-cost search 

When actions have different costs, an obvious choice is to use best-first search where the evaluation function is the cost of the path from the root to the current node. This is called Dijkstra’s algorithm by the theoretical computer science community, and uniform-cost search by the AI community.

The complexity of uniform-cost search is characterized in terms of \(C^*\) , the cost of the optimal solution, and \(\epsilon\) , a lower bound on the cost of each action, with \(\epsilon>0\) . Then the algorithm’s worst-case time and space complexity is \(O(b^{1+\lfloor C^*/\epsilon\rfloor})\) , which can be much greater than \(b^d\) .

When all action costs are equal, \(b^{1+\lfloor C^*/\epsilon\rfloor}\) is just \(b^{d+1}\) , and uniform-cost search is similar to breadth-first search.

3.4.3 Depth-first search and the problem of memory 

Depth-first search always expands the deepest node in the frontier first. It could be implemented as a call to \(Best\-First\-Search\) where the evaluation function \(f\) is the negative of the depth.

For problems where a tree-like search is feasible, depth-first search has much smaller needs for memory. A depth-first tree-like search takes time proportional to the number of states, and has memory complexity of only \(O(bm)\) , where \(b\) is the branching factor and \(m\) is the maximum depth of the tree.

A variant of depth-first search called backtracking search uses even less memory.

3.4.4 Depth-limited and iterative deepening search 

To keep depth-first search from wandering down an infinite path, we can use depth-limited search , a version of depth-first search in which we supply a depth limit, \(l\) , and treat all nodes at depth \(l\) as if they had no successors. The time complexity is \(O(b^l)\) and the space complexity is \(O(bl)\)

Iterative deepening search solves the problem of picking a good value for \(l\) by trying all values: first 0, then 1, then 2, and so on—until either a solution is found, or the depth- limited search returns the failure value rather than the cutoff value.

Its memory requirements are modest: \(O(bd)\) when there is a solution, or \(O(bm)\) on finite state spaces with no solution. The time complexity is \(O(bd)\) when there is a solution, or \(O(bm)\) when there is none.

In general, iterative deepening is the preferred uninformed search method when the search state space is larger than can fit in memory and the depth of the solution is not known .

3.4.5 Bidirectional search 

An alternative approach called bidirectional search simultaneously searches forward from the initial state and backwards from the goal state(s), hoping that the two searches will meet.

3.4.6 Comparing uninformed search algorithms 

3.5 Informed (Heuristic) Search Strategies 

An informed search strategy uses domain–specific hints about the location of goals to find colutions more efficiently than an uninformed strategy. The hints come in the form of a heuristic function , denoted \(h(n)\) :

\(h(n)\) = estimated cost of the cheapest path from the state at node \(n\) to a goal state.

3.5.1 Greedy best-first search 

Greedy best-first search is a form of best-first search that expands first the node with the lowest \(h(n)\) value—the node that appears to be closest to the goal—on the grounds that this is likely to lead to a solution quickly. So the evaluation function \(f(n)=h(n)\) .

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Problem-Solving Agents In Artificial Intelligence

In artificial intelligence, a problem-solving agent refers to a type of intelligent agent designed to address and solve complex problems or tasks in its environment. These agents are a fundamental concept in AI and are used in various applications, from game-playing algorithms to robotics and decision-making systems. Here are some key characteristics and components of a problem-solving agent:

• Perception : Problem-solving agents typically have the ability to perceive or sense their environment. They can gather information about the current state of the world, often through sensors, cameras, or other data sources.
• Knowledge Base : These agents often possess some form of knowledge or representation of the problem domain. This knowledge can be encoded in various ways, such as rules, facts, or models, depending on the specific problem.
• Reasoning : Problem-solving agents employ reasoning mechanisms to make decisions and select actions based on their perception and knowledge. This involves processing information, making inferences, and selecting the best course of action.
• Planning : For many complex problems, problem-solving agents engage in planning. They consider different sequences of actions to achieve their goals and decide on the most suitable action plan.
• Actuation : After determining the best course of action, problem-solving agents take actions to interact with their environment. This can involve physical actions in the case of robotics or making decisions in more abstract problem-solving domains.
• Feedback : Problem-solving agents often receive feedback from their environment, which they use to adjust their actions and refine their problem-solving strategies. This feedback loop helps them adapt to changing conditions and improve their performance.
• Learning : Some problem-solving agents incorporate machine learning techniques to improve their performance over time. They can learn from experience, adapt their strategies, and become more efficient at solving similar problems in the future.

Problem-solving agents can vary greatly in complexity, from simple algorithms that solve straightforward puzzles to highly sophisticated AI systems that tackle complex, real-world problems. The design and implementation of problem-solving agents depend on the specific problem domain and the goals of the AI application.

Hello, I’m Hridhya Manoj. I’m passionate about technology and its ever-evolving landscape. With a deep love for writing and a curious mind, I enjoy translating complex concepts into understandable, engaging content. Let’s explore the world of tech together

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Lecture 2: reasoning: goal trees and problem solving.

Description: This lecture covers a symbolic integration program from the early days of AI. We use safe and heuristic transformations to simplify the problem, and then consider broader questions of how much knowledge is involved, and how the knowledge is represented.

Instructor: Patrick H. Winston

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AI accelerates problem-solving in complex scenarios

By adam zewe.

December 5, 2023 | MIT News

While Santa Claus may have a magical sleigh and nine plucky reindeer to help him deliver presents, for companies like FedEx, the optimization problem of efficiently routing holiday packages is so complicated that they often employ specialized software to find a solution.

This software, called a mixed-integer linear programming (MILP) solver, splits a massive optimization problem into smaller pieces and uses generic algorithms to try and find the best solution. However, the solver could take hours — or even days — to arrive at a solution.

The process is so onerous that a company often must stop the software partway through, accepting a solution that is not ideal but the best that could be generated in a set amount of time.

Researchers from MIT and ETH Zurich used machine learning to speed things up.

They identified a key intermediate step in MILP solvers that has so many potential solutions it takes an enormous amount of time to unravel, which slows the entire process. The researchers employed a filtering technique to simplify this step, then used machine learning to find the optimal solution for a specific type of problem.

Their data-driven approach enables a company to use its own data to tailor a general-purpose MILP solver to the problem at hand.

This new technique sped up MILP solvers between 30 and 70 percent, without any drop in accuracy. One could use this method to obtain an optimal solution more quickly or, for especially complex problems, a better solution in a tractable amount of time.

This approach could be used wherever MILP solvers are employed, such as by ride-hailing services, electric grid operators, vaccination distributors, or any entity faced with a thorny resource-allocation problem.

“Sometimes, in a field like optimization, it is very common for folks to think of solutions as either purely machine learning or purely classical. I am a firm believer that we want to get the best of both worlds, and this is a really strong instantiation of that hybrid approach,” says senior author Cathy Wu, the Gilbert W. Winslow Career Development Assistant Professor in Civil and Environmental Engineering (CEE), and a member of a member of the Laboratory for Information and Decision Systems (LIDS) and the Institute for Data, Systems, and Society (IDSS).

Wu wrote the  paper  with co-lead authors Sirui Li, an IDSS graduate student, and Wenbin Ouyang, a CEE graduate student; as well as Max Paulus, a graduate student at ETH Zurich. The research will be presented at the Conference on Neural Information Processing Systems.

Tough to solve

MILP problems have an exponential number of potential solutions. For instance, say a traveling salesperson wants to find the shortest path to visit several cities and then return to their city of origin. If there are many cities which could be visited in any order, the number of potential solutions might be greater than the number of atoms in the universe.  

“These problems are called NP-hard, which means it is very unlikely there is an efficient algorithm to solve them. When the problem is big enough, we can only hope to achieve some suboptimal performance,” Wu explains.

An MILP solver employs an array of techniques and practical tricks that can achieve reasonable solutions in a tractable amount of time.

A typical solver uses a divide-and-conquer approach, first splitting the space of potential solutions into smaller pieces with a technique called branching. Then, the solver employs a technique called cutting to tighten up these smaller pieces so they can be searched faster.

Cutting uses a set of rules that tighten the search space without removing any feasible solutions. These rules are generated by a few dozen algorithms, known as separators, that have been created for different kinds of MILP problems. 

Wu and her team found that the process of identifying the ideal combination of separator algorithms to use is, in itself, a problem with an exponential number of solutions.

“Separator management is a core part of every solver, but this is an underappreciated aspect of the problem space. One of the contributions of this work is identifying the problem of separator management as a machine learning task to begin with,” she says.

Shrinking the solution space

She and her collaborators devised a filtering mechanism that reduces this separator search space from more than 130,000 potential combinations to around 20 options. This filtering mechanism draws on the principle of diminishing marginal returns, which says that the most benefit would come from a small set of algorithms, and adding additional algorithms won’t bring much extra improvement.

Then they use a machine-learning model to pick the best combination of algorithms from among the 20 remaining options.

This model is trained with a dataset specific to the user’s optimization problem, so it learns to choose algorithms that best suit the user’s particular task. Since a company like FedEx has solved routing problems many times before, using real data gleaned from past experience should lead to better solutions than starting from scratch each time.

The model’s iterative learning process, known as contextual bandits, a form of reinforcement learning, involves picking a potential solution, getting feedback on how good it was, and then trying again to find a better solution.

This data-driven approach accelerated MILP solvers between 30 and 70 percent without any drop in accuracy. Moreover, the speedup was similar when they applied it to a simpler, open-source solver and a more powerful, commercial solver.

In the future, Wu and her collaborators want to apply this approach to even more complex MILP problems, where gathering labeled data to train the model could be especially challenging. Perhaps they can train the model on a smaller dataset and then tweak it to tackle a much larger optimization problem, she says. The researchers are also interested in interpreting the learned model to better understand the effectiveness of different separator algorithms.

This research is supported, in part, by Mathworks, the National Science Foundation (NSF), the MIT Amazon Science Hub, and MIT’s Research Support Committee.

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The Intersection of Math and AI: A New Era in Problem-Solving

Conference is exploring burgeoning connections between the two fields.

Traditionally, mathematicians jot down their formulas using paper and pencil, seeking out what they call pure and elegant solutions. In the 1970s, they hesitantly began turning to computers to assist with some of their problems. Decades later, computers are often used to crack the hardest math puzzles. Now, in a similar vein, some mathematicians are turning to machine learning tools to aid in their numerical pursuits.

Embracing Machine Learning in Mathematics

“Mathematicians are beginning to embrace machine learning,” says Sergei Gukov, the John D. MacArthur Professor of Theoretical Physics and Mathematics at Caltech, who put together the Mathematics and Machine Learning 2023 conference, which is taking place at Caltech December 10–13.

“There are some mathematicians who may still be skeptical about using the tools,” Gukov says. “The tools are mischievous and not as pure as using paper and pencil, but they work.”

Machine Learning: A New Era in Mathematical Problem Solving

Machine learning is a subfield of AI, or artificial intelligence , in which a computer program is trained on large datasets and learns to find new patterns and make predictions. The conference, the first put on by the new Richard N. Merkin Center for Pure and Applied Mathematics, will help bridge the gap between developers of machine learning tools (the data scientists) and the mathematicians. The goal is to discuss ways in which the two fields can complement each other.

Mathematics and Machine Learning: A Two-Way Street

“It’s a two-way street,” says Gukov, who is the director of the new Merkin Center, which was established by Caltech Trustee Richard Merkin.

“Mathematicians can help come up with clever new algorithms for machine learning tools like the ones used in generative AI programs like ChatGPT, while machine learning can help us crack difficult math problems.”

Yi Ni, a professor of mathematics at Caltech, plans to attend the conference, though he says he does not use machine learning in his own research, which involves the field of topology and, specifically, the study of mathematical knots in lower dimensions. “Some mathematicians are more familiar with these advanced tools than others,” Ni says. “You need to know somebody who is an expert in machine learning and willing to help. Ultimately, I think AI for math will become a subfield of math.”

The Riemann Hypothesis and Machine Learning

One tough problem that may unravel with the help of machine learning, according to Gukov, is known as the Riemann hypothesis. Named after the 19th-century mathematician Bernhard Riemann, this problem is one of seven Millennium Problems selected by the Clay Mathematics Institute; a $1 million prize will be awarded for the solution to each problem.

The Riemann hypothesis centers around a formula known as the Riemann zeta function, which packages information about prime numbers. If proved true, the hypothesis would provide a new understanding of how prime numbers are distributed. Machine learning tools could help crack the problem by providing a new way to run through more possible iterations of the problem.

Mathematicians and Machine Learning: A Synergistic Relationship

“Machine learning tools are very good at recognizing patterns and analyzing very complex problems,” Gukov says.

Ni agrees that machine learning can serve as a helpful assistant. “Machine learning solutions may not be as beautiful, but they can find new connections,” he says. “But you still need a mathematician to turn the questions into something computers can solve.”

Knot Theory and Machine Learning

Gukov has used machine learning himself to untangle problems in knot theory. Knot theory is the study of abstract knots, which are similar to the knots you might find on a shoestring, but the ends of the strings are closed into loops. These mathematical knots can be entwined in various ways, and mathematicians like Gukov want to understand their structures and how they relate to each other. The work has relationships to other fields of mathematics such as representation theory and quantum algebra, and even quantum physics.

In particular, Gukov and his colleagues are working to solve what is called the smooth Poincaré conjecture in four dimensions. The original Poincaré conjecture, which is also a Millennium Problem, was proposed by mathematician Henri Poincaré early in the 20th century. It was ultimately solved from 2002 to 2003 by Grigori Perelman (who famously turned down his prize of $1 million). The problem involves comparing spheres to certain types of manifolds that look like spheres; manifolds are shapes that are projections of higher-dimensional objects onto lower dimensions. Gukov says the problem is like asking, “Are objects that look like spheres really spheres?”

The four-dimensional smooth Poincaré conjecture holds that, in four dimensions, all manifolds that look like spheres are indeed actually spheres. In an attempt to solve this conjecture, Gukov and his team develop a machine learning approach to evaluate so-called ribbon knots.

“Our brain cannot handle four dimensions, so we package shapes into knots,” Gukov says. “A ribbon is where the string in a knot pierces through a different part of the string in three dimensions but doesn’t pierce through anything in four dimensions. Machine learning lets us analyze the ‘ribboness’ of knots, a yes-or-no property of knots that has applications to the smooth Poincaré conjecture.”

“This is where machine learning comes to the rescue,” writes Gukov and his team in a preprint paper titled “ Searching for Ribbons with Machine Learning .” “It has the ability to quickly search through many potential solutions and, more importantly, to improve the search based on the successful ‘games’ it plays. We use the word ‘games’ since the same types of algorithms and architectures can be employed to play complex board games, such as Go or chess, where the goals and winning strategies are similar to those in math problems.”

The Interplay of Mathematics and Machine Learning Algorithms

On the flip side, math can help in developing machine learning algorithms, Gukov explains. A mathematical mindset, he says, can bring fresh ideas to the development of the algorithms behind AI tools. He cites Peter Shor as an example of a mathematician who brought insight to computer science problems. Shor, who graduated from Caltech with a bachelor’s degree in mathematics in 1981, famously came up with what is known as Shor’s algorithm, a set of rules that could allow quantum computers of the future to factor integers faster than typical computers, thereby breaking digital encryption codes.

Today’s machine learning algorithms are trained on large sets of data. They churn through mountains of data on language, images, and more to recognize patterns and come up with new connections. However, data scientists don’t always know how the programs reach their conclusions. The inner workings are hidden in a so-called “black box.” A mathematical approach to developing the algorithms would reveal what’s happening “under the hood,” as Gukov says, leading to a deeper understanding of how the algorithms work and thus can be improved.

“Math,” says Gukov, “is fertile ground for new ideas.”

The conference will take place at the Merkin Center on the eighth floor of Caltech Hall.

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Characteristics of Artificial Intelligence Problems

Problems in Artificial Intelligence (AI) come in different forms, each with its own set of challenges and potential for innovation. From image recognition to natural language processing, AI problems exhibit distinct characteristics that shape the strategies and techniques used to tackle them effectively. In this article, we delve into the fundamental characteristics of AI problems, providing light on what makes them so fascinating and formidable.

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Key Terminologies in Artificial Intelligence Problems

Addressing the challenges of ai problems, examples of ai applications and challenges across domains, characteristics of artificial intelligence problems – faqs.

Before exploring the characteristics, let’s clarify some essential AI concepts:

• Problem-solving: Problem-solving is a process that is a solution provided to a complex problem or task. When dealing with AI, problem-solving involves creating algorithms and methods of artificial intelligence that will empower machines to imitate humans’ capabilities of logical and reasonable thinking in certain situations.
• Search Space: Searching space refers to the area where an agent involved in the problem-solving process can examine all the possible states or settings with the hope of discovering a solution. It covers a gamut of options that the agent might select for arriving at the same destination.
• State: An entity represents some unique and specific arrangement of elements in a problem-solving situation. States can be assigned to different locations, challenges, or dangers that the problem-solving agent faces while looking for a solution to the problem within the search space.
• Search Algorithm: A search algorithm describes any process or method targeted for examining and exploring the given problem space to find a solution. Algorithm decision-making has diverging levels of complexity and effectiveness. They are studied to help in the discovery of the most suitable results.
• Heuristic: Heuristic is a thumb rule or guiding principle that is used to make intelligent decisions or solve the problems that are encountered during the process. Applying heuristics in AI is prevalent in prioritizing search paths or evaluating probable solutions based on their likelihood of finishing successfully.
• Optimization: The problem of optimization implies finding the best solution for process selection among the set of feasible alternatives submitted to some previously set objectives or criteria. AI optimization approaches are employed to deal optimally with complex issues through performance and efficiency improvement.

By understanding these key terminologies, we can better grasp the characteristics of AI problems and the techniques used to address them. These concepts form the foundation of AI problem-solving and provide the framework for developing innovative solutions to real-world challenges.

Let’s explore the core characteristics that differentiate AI problems:

• Learning and adaptation: AI systems should be capable of learning from data or experiences and adapting their behaviour accordingly. This enables them to improve performance over time and handle new situations more effectively.
• Complexity: AI problems often involve dealing with complex systems or large amounts of data. AI systems must be able to handle this complexity efficiently to produce meaningful results.
• Uncertainty: AI systems frequently operate in environments where outcomes are uncertain or incomplete information is available. They must be equipped to make decisions or predictions under such conditions.
• Dynamism: Environments in which AI systems operate can change over time. These changes may occur unpredictably or according to specific rules, requiring AI systems to continually adjust their strategies or models.
• Interactivity : Many AI applications involve interaction with users or other agents. Effective AI systems should be able to perceive, interpret, and respond to these interactions in a meaningful way.
• Context dependence: The behavior or performance of AI systems may depend on the context in which they operate. Understanding and appropriately responding to different contexts is essential for achieving desired outcomes.
• Multi-disciplinary: AI problems often require knowledge and techniques from multiple disciplines, including computer science, mathematics, statistics, psychology, and more. Integrating insights from these diverse fields is necessary for developing effective AI solutions.
• Goal-oriented Design: AI systems are typically designed to achieve specific objectives or goals. Designing AI systems with clear objectives in mind helps guide the development process and ensures that the resulting systems are focused on achieving meaningful outcomes.

These characteristics collectively shape the challenges and opportunities involved in developing and deploying AI systems across various domains and applications.

The characteristics of AI problems present unique challenges that require innovative approaches to solution development. Some of the key aspects to consider in tackling these challenges include:

• Complexity and Uncertainty: AI difficulties are sometimes characterized by highly variable domains that are difficult to predict exactly. Hence, AI algorithms should be installed with the skill of dealing with unclear circumstances and should make decisions that are based on imperfect data or noisy information.
• Algorithmic Efficiency: Among the key challenges of this approach are the enormous search spaces, computational resources, and the efficiency of the algorithms in terms of problem-solving. Strategies like caching, pruning, and parallelization are among the most widely used implementations for better algorithmic speed.
• Domain Knowledge Integration: Such numerous AI problems involve the ability to capture the rules and reasoning of the real world to model and solve the questions correctly. The AI machines that have been trained with expertise from relevant domains improve the accuracy and effectiveness of the applications in the real world.
• Scalability and Adaptability: AI solutions should be able to process large datasets and complex cases at the same time, and they should also be versatile by responding to shifts in conditions and requirements. Strategies such as machine learning and reinforcement learning allow systems to do more than just perform according to the given tasks at hand; they empower systems to learn and progress over time.
• Ethical and Social Implications: AI technologies elicit ethical and social limitations concerning problems of bias, justice, privacy, and responsible office. Taking these implications into account, along with ethical frameworks, compliance frameworks, and stakeholder engagement, is essential. This approach will help position cryptocurrencies as a secure and trustworthy investment.
• Interpretability and Explainability: To achieve interpretability and explainability of AI algorithms for the sake of understanding and confidence among users and stakeholders, these algorithms should be knowable and comprehensible enough. Examples like chatbots producing natural-like conversation could better clarify the working scheme of AI technology.
• Robustness and Resilience: AI machinery should perform against its being hacked or affected by adversarial attacks, inaccuracies (errors), and environmental changes. Robustness testing, the construction of mechanisms for error handling, and the building up of redundancy must be taken seriously by AI systems to ensure their reliability and stability.
• Human-AI Collaboration: Successful human-AI entente is the key component to making the most of our advantages as well as artificial intelligence skills. Achieving AI solutions that are capable of supporting human skills and more importantly, preferences will reduce human efforts correspondingly and bring the best performance.

By addressing these challenges through innovative methodologies and interdisciplinary collaboration, we can harness the full potential of AI to solve complex problems and drive societal progress.

1. Robotics

Problem: A delivery robot navigating a busy warehouse to locate and retrieve a specific item.

Characteristics:

• Complexity: Industrial storage is networked, in the middle of things, with obstacles, and other robots and people moving unpredictably. This robot must process the visual scene, plan the route effectively, and detect and avoid possible collisions.
• Dynamism: A combination of outside factors leads to change, which is a constant inside the warehouse. Unpredictable system failures or spontaneous tasks can make the robot change its means and decision-making at the moment of need.
• Uncertainty: Sensor data (such as images obtained from a camera) might be noisy, incomplete, and unstable. The robot could be handling decisions based on fragmented or formless pieces of information.

2. Natural Language Processing (NLP)

Problem: A sentiment analysis system in NLP classifying customer reviews as positive, negative, or neutral.

• Subjectivity: Human language is nuanced. Sarcasm, irony, and figurative expressions can be difficult for machines to accurately interpret.
• Need for Context: Understanding sentiment may depend on cultural references, product-specific knowledge, or even the reviewer’s prior interactions with the company.
• Ambiguity: A single word or phrase could have multiple meanings, affecting the overall sentiment of the text.

3. Computer Vision

Problem: A medical image recognition system in Computer Vision designed to detect tumors in X-rays or MRI scans.

• Complexity: Medical images are highly detailed and can exhibit subtle variations. The system needs to distinguish between healthy tissue and potential abnormalities.
• Uncertainty: Images may contain noise or artifacts. The presence of a tumor might not be immediately obvious, requiring the system to handle ambiguity.
• Ethical Considerations: False positives or false negatives have serious consequences for patient health. Accuracy, transparency, and minimizing bias are crucial.

The premises of AI-based problems – complexity, uncertainty, subjectivity, and more, – bring an unavoidable difficulty to the table. These features must be known for building appropriate AI because this is necessary. Through the use of machine learning, probabilistic reasoning, and knowledge representation which are referred to as the tools in AI development alongside the ethical considerations, these designers and scientists can face such complexities well and give shape to AI in a way that will be beneficial to society.

Q. What are the core characteristics that differentiate AI problems?

The core characteristics of AI problems include complexity, uncertainty and ambiguity, lack of clear problem definition, non-linearity, dynamism, subjectivity, interactivity, context sensitivity, and ethical considerations.

Q. Can you explain the concept of problem-solving in AI?

Problem-solving in AI involves creating algorithms and methods that enable machines to imitate human capabilities of logical and reasonable thinking in certain situations.

Q. What is meant by the term “search space” in AI?

Search space refers to the area where an agent involved in the problem-solving process can examine all the possible states or settings with the hope of discovering a solution.

Q. How do AI algorithms address challenges such as complexity and uncertainty?

AI algorithms are designed to handle unclear circumstances and make decisions based on imperfect data or noisy information.

Q. What are some examples of AI applications and the challenges they face?

Examples include robotics (e.g., delivery robots navigating busy warehouses), natural language processing (e.g., sentiment analysis of customer reviews), and computer vision (e.g., medical image recognition for detecting tumors).

Q. What role do ethical considerations play in AI development?

Ethical considerations are crucial in AI development to address issues such as bias, justice, privacy, and responsibility, ensuring that AI technologies are deployed responsibly and ethically.

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Artificial intelligence is the ability of a computer or computer-controlled robot to perform tasks that are commonly associated with the  intellectual processes characteristic of humans , such as the ability to reason. Although there are as yet no AIs that match full human flexibility over wider domains or in tasks requiring much everyday knowledge, some AIs perform specific tasks as well as humans. Learn more.

Are artificial intelligence and machine learning the same?

No, artificial intelligence and machine learning are not the same, but they are closely related. Machine learning is the method to train a computer to learn from its inputs but without explicit programming for every circumstance. Machine learning helps a computer to achieve artificial intelligence.

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artificial intelligence (AI) , the ability of a digital computer or computer-controlled robot to perform tasks commonly associated with intelligent beings. The term is frequently applied to the project of developing systems endowed with the intellectual processes characteristic of humans, such as the ability to reason, discover meaning, generalize, or learn from past experience. Since their development in the 1940s, digital computers have been programmed to carry out very complex tasks—such as discovering proofs for mathematical theorems or playing chess —with great proficiency. Despite continuing advances in computer processing speed and memory capacity, there are as yet no programs that can match full human flexibility over wider domains or in tasks requiring much everyday knowledge. On the other hand, some programs have attained the performance levels of human experts and professionals in executing certain specific tasks, so that artificial intelligence in this limited sense is found in applications as diverse as medical diagnosis , computer search engines , voice or handwriting recognition, and chatbots .

What is intelligence?

Artificial intelligence is changing how we interact online, how we manage our finances, and even how we work. Learn more with Britannica Money .

• Using AI for money management
• How AI is changing work
• Ethical questions and AI
• AI and regulation
• Investing in AI stocks

All but the simplest human behavior is ascribed to intelligence, while even the most complicated insect behavior is usually not taken as an indication of intelligence. What is the difference? Consider the behavior of the digger wasp , Sphex ichneumoneus . When the female wasp returns to her burrow with food, she first deposits it on the threshold , checks for intruders inside her burrow, and only then, if the coast is clear, carries her food inside. The real nature of the wasp’s instinctual behavior is revealed if the food is moved a few inches away from the entrance to her burrow while she is inside: on emerging, she will repeat the whole procedure as often as the food is displaced. Intelligence—conspicuously absent in the case of the wasp—must include the ability to adapt to new circumstances.

(Read Ray Kurzweil’s Britannica essay on the future of “Nonbiological Man.”)

Psychologists generally characterize human intelligence not by just one trait but by the combination of many diverse abilities. Research in AI has focused chiefly on the following components of intelligence: learning, reasoning, problem solving , perception , and using language.

There are a number of different forms of learning as applied to artificial intelligence. The simplest is learning by trial and error. For example, a simple computer program for solving mate-in-one chess problems might try moves at random until mate is found. The program might then store the solution with the position so that, the next time the computer encountered the same position, it would recall the solution. This simple memorizing of individual items and procedures—known as rote learning—is relatively easy to implement on a computer. More challenging is the problem of implementing what is called generalization . Generalization involves applying past experience to analogous new situations. For example, a program that learns the past tense of regular English verbs by rote will not be able to produce the past tense of a word such as jump unless the program was previously presented with jumped , whereas a program that is able to generalize can learn the “add -ed ” rule for regular verbs ending in a consonant and so form the past tense of jump on the basis of experience with similar verbs.

(Read Yuval Noah Harari’s Britannica essay on the future of “Nonconscious Man.”)

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When Should You Use AI to Solve Problems?

Not every challenge requires an algorithmic approach.

AI is increasingly informing business decisions but can be misused if executives stick with old decision-making styles. A key to effective collaboration is to recognize which parts of a problem to hand off to the AI and which the managerial mind will be better at solving. While AI is superior at data-intensive prediction problems, humans are uniquely suited to the creative thought experiments that underpin the best decisions.

Business leaders often pride themselves on their intuitive decision-making. They didn’t get to be division heads and CEOs by robotically following some leadership checklist. Of course, intuition and instinct can be important leadership tools, but not if they’re indiscriminately applied.

• Bob Suh is the founder and CEO of OnCorps, which provides AI-based decision guidance systems to the financial services industry. The firm works with leading scientists at Yale, Oxford, and Harvard to test decision making and behavioral algorithms. Previously, he was the chief technology strategist at Accenture.

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• Published: 25 January 2022

Intelligent problem-solving as integrated hierarchical reinforcement learning

• Manfred Eppe   ORCID: orcid.org/0000-0002-5473-3221 1   nAff4 ,
• Christian Gumbsch   ORCID: orcid.org/0000-0003-2741-6551 2 , 3 ,
• Matthias Kerzel 1 ,
• Phuong D. H. Nguyen 1 ,
• Martin V. Butz   ORCID: orcid.org/0000-0002-8120-8537 2 &
• Stefan Wermter 1  

Nature Machine Intelligence volume  4 ,  pages 11–20 ( 2022 ) Cite this article

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• Cognitive control
• Computational models
• Computer science
• Learning algorithms
• Problem solving

According to cognitive psychology and related disciplines, the development of complex problem-solving behaviour in biological agents depends on hierarchical cognitive mechanisms. Hierarchical reinforcement learning is a promising computational approach that may eventually yield comparable problem-solving behaviour in artificial agents and robots. However, so far, the problem-solving abilities of many human and non-human animals are clearly superior to those of artificial systems. Here we propose steps to integrate biologically inspired hierarchical mechanisms to enable advanced problem-solving skills in artificial agents. We first review the literature in cognitive psychology to highlight the importance of compositional abstraction and predictive processing. Then we relate the gained insights with contemporary hierarchical reinforcement learning methods. Interestingly, our results suggest that all identified cognitive mechanisms have been implemented individually in isolated computational architectures, raising the question of why there exists no single unifying architecture that integrates them. As our final contribution, we address this question by providing an integrative perspective on the computational challenges to develop such a unifying architecture. We expect our results to guide the development of more sophisticated cognitively inspired hierarchical machine learning architectures.

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Acknowledgements

We acknowledge funding from the DFG (projects IDEAS, LeCAREbot, TRR169, SPP 2134, RTG 1808 and EXC 2064/1), the Humboldt Foundation and Max Planck Research School IMPRS-IS.

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Manfred Eppe

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Eppe, M., Gumbsch, C., Kerzel, M. et al. Intelligent problem-solving as integrated hierarchical reinforcement learning. Nat Mach Intell 4 , 11–20 (2022). https://doi.org/10.1038/s42256-021-00433-9

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How leaders are using ai as a problem-solving tool.

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Leaders face more complex decisions than ever before. For example, many must deliver new and better services for their communities while meeting sustainability and equity goals. At the same time, many need to find ways to operate and manage their budgets more efficiently. So how can these leaders make complex decisions and get them right in an increasingly tricky business landscape? The answer lies in harnessing technological tools like Artificial Intelligence (AI).

CHONGQING, CHINA - AUGUST 22: A visitor interacts with a NewGo AI robot during the Smart China Expo ... [+] 2022 on August 22, 2022 in Chongqing, China. The expo, held annually in Chongqing since 2018, is a platform to promote global exchanges of smart technologies and international cooperation in the smart industry. (Photo by Chen Chao/China News Service via Getty Images)

What is AI?

AI can help leaders in several different ways. It can be used to process and make decisions on large amounts of data more quickly and accurately. AI can also help identify patterns and trends that would otherwise be undetectable. This information can then be used to inform strategic decision-making, which is why AI is becoming an increasingly important tool for businesses and governments. A recent study by PwC found that 52% of companies accelerated their AI adoption plans in the last year. In addition, 86% of companies believe that AI will become a mainstream technology at their company imminently. As AI becomes more central in the business world, leaders need to understand how this technology works and how they can best integrate it into their operations.

At its simplest, AI is a computer system that can learn and work independently without human intervention. This ability makes AI a powerful tool. With AI, businesses and public agencies can automate tasks, get insights from data, and make decisions with little or no human input. Consequently, AI can be a valuable problem-solving tool for leaders across the private and public sectors, primarily through three methods.

1) Automation

One of AI’s most beneficial ways to help leaders is by automating tasks. This can free up time to focus on other essential things. For example, AI can help a city save valuable human resources by automating parking enforcement. In addition, this will help improve the accuracy of detecting violations and prevent costly mistakes. Automation can also help with things like appointment scheduling and fraud detection.

2) Insights from data

Another way AI can help leaders solve problems is by providing insights from data. With AI, businesses can gather large amounts of data and then use that data to make better decisions. For example, suppose a company is trying to decide which products to sell. In that case, AI can be used to gather data about customer buying habits and then use that data to make recommendations about which products to market.

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3) Simulations

Finally, AI can help leaders solve problems by allowing them to create simulations. With AI, organizations can test out different decision scenarios and see what the potential outcomes could be. This can help leaders make better decisions by examining the consequences of their choices. For example, a city might use AI to simulate different traffic patterns to see how a new road layout would impact congestion.

Choosing the Right Tools

Artificial intelligence and machine learning technologies can revolutionize how governments and businesses solve real-world problems,” said Chris Carson, CEO of Hayden AI, a global leader in intelligent enforcement technologies powered by artificial intelligence. His company addresses a problem once thought unsolvable in the transit world: managing illegal parking in bus lanes in a cost effective, scalable way.

Illegal parking in bus lanes is a major problem for cities and their transit agencies. Cars and trucks illegally parked in bus lanes force buses to merge into general traffic lanes, significantly slowing down transit service and making riders’ trips longer. That’s where a company like Hayden AI comes in. “Hayden AI uses artificial intelligence and machine learning algorithms to detect and process illegal parking in bus lanes in real-time so that cities can take proactive measures to address the problem ,” Carson observes.

Illegal parking in bus lanes is a huge problem for transit agencies. Hayden AI works with transit ... [+] agencies to fix this problem by installing its AI-powered camera systems on buses to conduct automated enforcement of parking violations in bus lanes

In this case, an AI-powered camera system is installed on each bus. The camera system uses computer vision to “watch” the street for illegal parking in the bus lane. When it detects a traffic violation, it sends the data back to the parking authority. This allows the parking authority to take action, such as sending a ticket to the offending vehicle’s owner.

The effectiveness of AI is entirely dependent on how you use it. As former Accenture chief technology strategist Bob Suh notes in the Harvard Business Review, problem-solving is best when combined with AI and human ingenuity. “In other words, it’s not about the technology itself; it’s about how you use the technology that matters. AI is not a panacea for all ills. Still, when incorporated into a company’s problem-solving repertoire, it can be an enormously powerful tool,” concludes Terence Mauri, founder of Hack Future Lab, a global think tank.

Split the Responsibility

Huda Khan, an academic researcher from the University of Aberdeen, believes that AI is critical for international companies’ success, especially in the era of disruption. Khan is calling international marketing academics’ research attention towards exploring such transformative approaches in terms of how these inform competitive business practices, as are international marketing academics Michael Christofi from the Cyprus University of Technology; Richard Lee from the University of South Australia; Viswanathan Kumar from St. John University; and Kelly Hewett from the University of Tennessee. “AI is very good at automating repetitive tasks, such as customer service or data entry. But it’s not so good at creative tasks, such as developing new products,” Khan says. “So, businesses need to think about what tasks they want to automate and what tasks they want to keep for humans.”

Khan believes that businesses need to split the responsibility between AI and humans. For example, Hayden AI’s system is highly accurate and only sends evidence packages of potential violations for human review. Once the data is sent, human analysis is still needed to make the final decision. But with much less work to do, government agencies can devote their employees to tasks that can’t be automated.

Backed up by efficient, effective data analysis, human problem-solving can be more innovative than ever. Like all business transitions, developing the best system for combining human and AI work might take some experimentation, but it can significantly impact future success. For example, if a company is trying to improve its customer service, it can use AI startup Satisfi’s natural language processing technology . This technology can understand a customer’s question and find the best answer from a company’s knowledge base. Likewise, if a company tries to increase sales, it can use AI startup Persado’s marketing language generation technology . This technology can be used to create more effective marketing campaigns by understanding what motivates customers and then generating language that is more likely to persuade them to make a purchase.

Look at the Big Picture

A technological solution can frequently improve performance in multiple areas simultaneously. For instance, Hayden AI’s automated enforcement system doesn’t just help speed up transit by keeping bus lanes clear for buses; it also increases data security by limiting how much data is kept for parking enforcement, which allows a city to increase the efficiency of its transportation while also protecting civil liberties.

This is the case with many technological solutions. For example, an e-commerce business might adopt a better data architecture to power a personalized recommendation option and benefit from improved SEO. As a leader, you can use your big-picture view of your company to identify critical secondary benefits of technologies. Once you have the technologies in use, you can also fine-tune your system to target your most important priorities at once.

In summary, AI technology is constantly evolving, becoming more accessible and affordable for businesses of all sizes. By harnessing the power of AI, leaders can make better decisions, improve efficiency, and drive innovation. However, it’s important to remember that AI is not a silver bullet. Therefore, organizations must use AI and humans to get the best results.

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