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Artificial Intelligence 3. Search in Problem Solving. Course V231 Department of Computing Imperial College, London Jeremy Gow. Problem Solving Agents. Looking to satisfy some goal Wants environment to be in particular state Have a number of possible actions An action changes environment
Artificial Intelligence 3. Search in Problem Solving Course V231 Department of Computing Imperial College, London Jeremy Gow
Problem Solving Agents • Looking to satisfy some goal • Wants environment to be in particular state • Have a number of possible actions • An action changes environment • What sequence of actions reaches the goal? • Many possible sequences • Agent must search through sequences
Examples of Search Problems • Chess • Each turn, search moves for win • Route finding • Search routes for one that reaches destination • Theorem proving (L6-9) • Search chains of reasoning for proof • Machine learning (L10-14) • Search through concepts for one which achieves target categorisation
Search Terminology • States: “places” the search can visit • Search space: the set of possible states • Search path • Sequence of states the agent actually visits • Solution • A state which solves the given problem • Either known or has a checkable property • May be more than one solution • Strategy • How to choose the next state in the path at any given state
Specifying a Search Problem 1. Initial state • Where the search starts 2. Operators • Function taking one state to another state • How the agent moves around search space 3. Goal test • How the agent knows if solution state found Search strategies apply operators to chosen states
Example: Chess • Initial state (right) • Operators • Moving pieces • Goal test • Checkmate • Can the king move without being taken?
Example: Route Finding • Initial state • City journey starts in • Operators • Driving from city to city • Goal test • Is current location the destination city? Liverpool Leeds Nottingham Manchester Birmingham London
General Search Considerations1. Artefact or Path? • Interested in solution only, or path which got there? • Route finding • Known destination, must find the route (path) • Anagram puzzle • Doesn’t matter how you find the word • Only the word itself (artefact) is important • Machine learning • Usually only the concept (artefact) is important • Theorem proving • The proof is a sequence (path) of reasoning steps
General Search Considerations2. Completeness • Task may require one, many or all solutions • E.g. how many different ways to get from A to B? • Complete search space contains all solutions • Exhaustive search explores entire space (assuming finite) • Complete search strategy will find solution if one exists • Pruning rules out certain operators in certain states • Space still complete if no solutions pruned • Strategy still complete if not all solutions pruned
General Search Considerations3. Soundness • A sound search contains only correct solutions • An unsound search contains incorrect solutions • Caused by unsound operators or goal check • Dangers • find solutions to problems with no solutions • find a route to an unreachable destination • prove a theorem which is actually false • (Not a problem if all your problems have solutions) • produce incorrect solution to problem
General Search Considerations4. Time & Space Tradeoffs • Fast programs can be written • But they often use up too much memory • Memory efficient programs can be written • But they are often slow • Different search strategies have different memory/speed tradeoffs
General Search Considerations5. Additional Information • Given initial state, operators and goal test • Can you give the agent additional information? • Uninformed search strategies • Have no additional information • Informed search strategies • Uses problem specific information • Heuristic measure (Guess how far from goal)
Graph and Agenda Analogies • Graph Analogy • States are nodes in graph, operators are edges • Expanding a node adds edges to new states • Strategy chooses which node to expand next • Agenda Analogy • New states are put onto an agenda (a list) • Top of the agenda is explored next • Apply operators to generate new states • Strategy chooses where to put new states on agenda
Example Search Problem • A genetics professor • Wants to name her new baby boy • Using only the letters D,N & A • Search through possible strings (states) • D,DN,DNNA,NA,AND,DNAN, etc. • 3 operators: add D, N or A onto end of string • Initial state is an empty string • Goal test • Look up state in a book of boys’ names, e.g. DAN
Uninformed Search Strategies • Breadth-first search • Depth-first search • Iterative deepening search • Bidirectional search • Uniform-cost search • Also known as blind search
Breadth-First Search • Every time a new state is reached • New states put on the bottom of the agenda • When state “NA” is reached • New states “NAD”, “NAN”, “NAA” added to bottom • These get explored later (possibly much later) • Graph analogy • Each node of depth d is fully expanded before any node of depth d+1 is looked at
Breadth-First Search • Branching rate • Average number of edges coming from a node (3 above) • Uniform Search • Every node has same number of branches (as above)
Depth-First Search • Same as breadth-first search • But new states are put at the top of agenda • Graph analogy • Expand deepest and leftmost node next • But search can go on indefinitely down one path • D, DD, DDD, DDDD, DDDDD, … • One solution to impose a depth limit on the search • Sometimes the limit is not required • Branches end naturally (i.e. cannot be expanded)
Depth-First Search (Depth Limit 4)
State- or Action-Based Definition? • Alternative ways to define strategies • Agenda stores (state, action) rather than state • Records “actions to perform” • Not “nodes expanded” • Only performs necessary actions • Changes node order • Textbook is state-oriented • Online notes action-oriented
Depth- v. Breadth-First Search • Suppose branching rate b • Breadth-first • Complete (guaranteed to find solution) • Requires a lot of memory • At depth d needs to remember up to bd-1 states • Depth-first • Not complete because of indefinite paths or depth limit • But is memory efficient • Only needs to remember up to b*d states
Iterative Deepening Search • Idea: do repeated depth first searches • Increasing the depth limit by one every time • DFS to depth 1, DFS to depth 2, etc. • Completely re-do the previous search each time • Most DFS effort is in expanding last line of the tree • e.g. to depth five, branching rate of 10 • DFS: 111,111 states, IDS: 123,456 states • Repetition of only 11% • Combines best of BFS and DFS • Complete and memory efficient • But slower than either
London Bidirectional Search Liverpool Leeds • If you know the solution state • Work forwards and backwards • Look to meet in middle • Only need to go to half depth • Difficulties • Do you really know solution? Unique? • Must be able to reverse operators • Record all paths to check they meet • Memory intensive Nottingham Manchester Birmingham Peterborough
Action and Path Costs • Action cost • Particular value associated with an action • Examples • Distance in route planning • Power consumption in circuit board construction • Path cost • Sum of all the action costs in the path • If action cost = 1 (always), then path cost = path length
Uniform-Cost Search • Breadth-first search • Guaranteed to find the shortest path to a solution • Not necessarily the least costly path • Uniform path cost search • Choose to expand node with the least path cost • Guaranteed to find a solution with least cost • If we know that path cost increases with path length • This method is optimal and complete • But can be very slow
Informed Search Strategies • Greedy search • A* search • IDA* search • Hill climbing • Simulated annealing • Also known as heuristic search • require heuristic function
Best-First Search • Evaluation function f gives cost for each state • Choose state with smallest f(state) (‘the best’) • Agenda: f decides where new states are put • Graph: f decides which node to expand next • Many different strategies depending on f • For uniform-cost search f = path cost • Informed search strategies defines f based on heuristic function
London Heuristic Functions • Estimate of path cost h • From state to nearest solution • h(state) >= 0 • h(solution) = 0 • Strategies can use this information • Example: straight line distance • As the crow flies in route finding • Where does h come from? • maths, introspection, inspection or programs (e.g. ABSOLVER) Liverpool Leeds 135 Nottingham 155 75 Peterborough 120
Greedy Search • Always take the biggest bite • f(state) = h(state) • Choose smallest estimated cost to solution • Ignores the path cost • Blind alley effect: early estimates very misleading • One solution: delay the use of greedy search • Not guaranteed to find optimal solution • Remember we are estimating the path cost to solution
A* Search • Path cost is g and heuristic function is h • f(state) = g(state) + h(state) • Choose smallest overall path cost (known + estimate) • Combines uniform-cost and greedy search • Can prove that A* is complete and optimal • But only if h is admissable, i.e. underestimates the true path cost from state to solution • See Russell and Norvig for proof
London A* Example: Route Finding • First states to try: • Birmingham, Peterborough • f(n) = distance from London + crow flies distance from state • i.e., solid + dotted line distances • f(Peterborough) = 120 + 155 = 275 • f(Birmingham) = 130 + 150 = 280 • Hence expand Peterborough • But must go through Leeds from Notts • So later Birmingham is better Liverpool Leeds 135 Nottingham 150 155 Birmingham Peterborough 130 120
IDA* Search • Problem with A* search • You have to record all the nodes • In case you have to back up from a dead-end • A* searches often run out of memory, not time • Use the same iterative deepening trick as IDS • But iterate over f(state) rather than depth • Define contours: f < 100, f < 200, f < 300 etc. • Complete & optimal as A*, but less memory
IDA* Search: Contours • Find all nodes • Where f(n) < 100 • Ignore f(n) >= 100 • Find all nodes • Where f(n) < 200 • Ignore f(n) >= 200 • And so on…
Hill Climbing & Gradient Descent • For artefact-only problems (don’t care about the path) • Depends on some e(state) • Hill climbing tries to maximise score e • Gradient descent tries to minimise cost e (the same strategy!) • Randomly choose a state • Only choose actions which improve e • If cannot improve e, then perform a random restart • Choose another random state to restart the search from • Only ever have to store one state (the present one) • Can’t have cycles as e always improves
Example: 8 Queens • Place 8 queens on board • So no one can “take” another • Gradient descent search • Throw queens on randomly • e = number of pairs which can attack each other • Move a queen out of other’s way • Decrease the evaluation function • If this can’t be done • Throw queens on randomly again
Simulated Annealing • Hill climbing can find local maxima/minima • C is local max, G is global max • E is local min, A is global min • Search must go wrong way to proceed! • Simulated annealing • Pick a random action • If action improves e then go with it • If not, choose with probability based on how bad it is • Can go the ‘wrong’ way • Effectively rules out really bad moves
Comparing Heuristic Searches • Effective branching rate • Idea: compare to a uniform search e.g. BFS • Where each node has same number of edges from it • Expanded n nodes to find solution at depth d • What would the branching rate be if uniform? • Effective branching factor b* • Use this formula to calculate it • n = 1 + b* + (b*)2 + (b*)3 + … + (b*)d • One heuristic function h1 dominates another h2 • If b* is always smaller for h1 than for h2
Example: Effective Branching Rate • Suppose a search has taken 52 steps • And found a solution at depth 5 • 52 = 1 + b* + (b*)2 + … + (b*)5 • So, using the mathematical equality from notes • We can calculate that b* = 1.91 • If instead, the agent • Had a uniform breadth first search • It would branch 1.91 times from each node
Uninformed Breadth-first search Depth-first search Iterative deepening Bidirectional search Uniform-cost search Informed Greedy search A* search IDA* search Hill climbing Simulated annealing SMA* in textbook Search Strategies
Problem Solving by Searching Search Methods : Local Search for Optimization Problems. 3. Beyond IDA*
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Register here to livestream Opening Day and Demo Day of FHFA’s Generative AI in Housing Finance TechSprint.
The FHFA Generative AI in Housing Finance TechSprint will be an in-person, team-based problem-solving event hosted by the Federal Housing Finance Agency’s (FHFA) Office of Financial Technology (OFT). The TechSprint will bring together technology, regulatory, housing, and consumer finance experts to identify use cases and associated control measures to support the responsible use of generative AI in housing finance.
Participants are organized into TechSprint teams and work over a three-day period to solve for problem statements centered around the question:
“How might the responsible use of generative AI promote a transparent, fair, equitable, and inclusive housing finance system, while fostering sustainable homeownership and rental opportunities?”
The TechSprint culminates in a Demo Day where each team will present its ideas to an independent panel of judges drawn from subject matter experts in government, industry, nonprofits, and academia.
The Generative AI in Housing Finance TechSprint will be held at FHFA’s Constitution Center headquarters in Washington, DC, and will run from July 22 to July 25, 2024. The application period to participate in-person at the TechSprint was open from March 20 through May 24, 2024.
Umbrella Statement
Generative artificial intelligence (AI) has captured the imagination and interest of a diverse set of stakeholders, including industry, government, and consumers. For the housing finance system, the transformative potential of generative AI extends beyond technological advancement. Generative AI presents an opportunity to promote a housing finance system that is transparent, fair, equitable, and inclusive and fosters sustainable homeownership. Realizing this potential, however, is contingent on a commitment to responsible innovation and ensuring that the development and use of generative AI is supported by ethical considerations and safety and soundness.
FHFA’s Generative AI in Housing Finance TechSprint challenges participants to address the question, “How might the responsible use of generative AI promote a transparent, fair, equitable, and inclusive housing finance system while fostering sustainable homeownership and rental opportunities?”
TechSprint participants will demonstrate:
Focused Statements
The four areas of focus are as follows:
Have additional questions about the 2024 TechSprint? Please contact OFT at [email protected] . To learn more about OFT, please visit the OFT home page . And to learn more about FHFA’s inaugural TechSprint held in 2023, please visit the Velocity TechSprint webpage .
Page Last Updated: May 28, 2024
For "CXO AI Playbook," Business Insider takes a look at mini case studies about AI adoption across industries, company sizes, and technology DNA. We've asked each of the featured companies to tell us about the problems they're trying to solve with AI, who's making these decisions internally, and their vision for using AI in the future.
Saatchi & Saatchi is a global communications and marketing agency that works with major brands , including Toyota and Tide. The agency, which is headquartered in London, is part of Publicis Communications , a hub of Publicis Groupe.
For each client and campaign, Saatchi & Saatchi creates a collection of assets, including images, videos, final presentations, strategic insights, and briefs. These items accumulate over the years as the agency continues working with clients, Jeremiah Knight, its chief operating officer, told Business Insider.
Often, teams need to review documents from past campaigns, such as when a company launches a product, he said, but the challenge is, "How do you find that stuff after you've created it?"
Sometimes, the people who worked on the original campaign can't remember where those documents are saved, or they might have left the agency, Knight added. Employees also don't always follow file-system hierarchies.
That can create a "needle in the haystack" situation to find necessary information, Knight said.
The agency realized that automation could help improve asset organization, Knight said, so he worked with the company's CEO and chief financial officer on a solution.
"Once you paint the picture of the problem and how valuable the solution might be, we all understood this would be a great thing for us to undertake," Knight added.
About two years ago, Saatchi & Saatchi contracted with Lucy , an AI-powered search engine, to help find specific items in its system.
Lucy is integrated into the agency's Microsoft Teams chat function. Users can ask it questions through Teams, and Lucy searches the agency's files and sends results in Teams, Knight said.
To access the documents, users are directed to log in to the Lucy web interface. They can also search and find information directly through the web interface without going through Teams.
"It's sort of a library of everything of our collective knowledge," Knight said, including creative assets, campaign data, and other information.
To help train the artificial-intelligence model to produce the desired results, the agency hosted trainings on how to use Lucy and encouraged everyone to use it and provide feedback.
"The more you play with it, the more you use it, the better it gets," Knight said. "We had to get over that hurdle to make sure that they continuously use it and help us train the model."
Lucy has helped Saatchi & Saatchi index information, Knight said. So if someone forgets to use the correct filing structure or saves information in the wrong place, the tool can usually find it.
"Not only is that a time saver, it actually is helping direct people straight to the documents that are the most valuable to answer the question, 'How can we learn from what we've done before?'" he said.
The AI implementation is still a work in progress , Knight added: "This is one of the most exciting times to play and experiment and see what's possible, unlock so many things creatively and workflow-wise for different departments."
Saatchi & Saatchi continues to leverage generative AI across its agency in multiple ways, such as creative conceptualizing , minimizing repetitive tasks, and analyzing data, Knight said.
He said the investment in the technology would continue as the agency sought to create efficiencies. In January, Publicis Groupe announced plans to invest $326 million in AI over the next three years, including a proprietary tool, CoreAI.
"AI helps with every single business problem," he said. "The less time you spend hunting for things, the faster you can create business value for your clients."
We want to hear from you. If you are interested in sharing your company's AI journey, email [email protected] .
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AI_03_Solving Problems by Searching.pptx. This document provides a summary of Lecture 3 on problem-solving by searching. It describes how problem-solving agents can formulate goals and problems, represent the problem as a state space, and find solutions using search algorithms like breadth-first search, uniform-cost search, depth-first search ...
Artificial Intelligence involves representing problems as state spaces and using algorithms to search the state space to solve the problem. The document discusses key concepts in problem solving using search including representing the problem as states, defining state transitions with successor functions, and exploring the resulting state space to find a solution.
The document discusses various problem solving techniques in artificial intelligence, including different types of problems, components of well-defined problems, measuring problem solving performance, and different search strategies.
Solving Problems By Searching Instructor: Dr Wei DingInstructor: Dr. Wei Ding Fall 2008 CS 470/670 Artificial Intelligence 1 Problem-Solving Agent yGoal-based agents: considering future actions and the desirability of their outcomes. yDecide what to do by finding sequences of actions
3 Problem-Solving Agents. Reach goals through sequences of actions Formulate the goal (s) and the problem Abstraction: Should be easier than original problem Search for a sequence of actions to reach a goal state A solution is a sequence of actions from initial state to a goal state Execute the sequence of actions. 4 Problem-Solving Agents.
CS461 Artificial Intelligence © Pinar Duygulu Spring 2008 5 Problem solving agents • An agent with several immediate options of unknown value
AUTOMATED PROBLEM SOLVING BY SEARCH • Generalized Techniques for Solving Large Classes of Complex Problems • Problem Statement is the Input and solution is the Output, sometimes even the problem specific algorithm or method could be the Output • Problem Formulation by AI Search Methods consists of the following key concepts ...
Artificial Intelligence Chapter 3: Solving Problems by Searching Michael Scherger Department of Computer Science Kent State University Problem Solving Agents Problem ... - A free PowerPoint PPT presentation (displayed as an HTML5 slide show) on PowerShow.com - id: 3e4dc2-NjIzM
Once a solution is obtained, another problem usually comes, and the cycle starts again. Searching techniques in problem-solving by using artificial intelligence (A.I) are surveyed in this paper. An overview of definitions, development and dimensions of A.I in the light of search for solutions to problems are accepted.
HEURISTIC SEARCH METHODS. BASICS OF STATE SPACE MODELLING ... Depending on the problem formulation, it can be a PATH from Start to Goal or a Sub- graph of And- ed
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.
AI3391 Session 5 Problem Solving Agent and searching for solutions. AI3391 Session 5 Problem Solving Agent and searching for solutions ... Proceedings from the 2nd World Conference on Artificial Intelligence, Machine Learning and Data Science October 19 - 20 , 2023 | Paris, France. How AI will transform eGov and Smart Cities (page 47)
The description offers insights into the critical concepts and strategies that power AI's ability to find solutions efficiently and effectively in various domains. In "Problem-Solving Strategies in Artificial Intelligence," we dive deeper into the foundational techniques and methodologies that AI systems rely on to tackle challenging problems.
Basic Search Algorithms • uninformed( Blind) search: breadth-first, depth-first, depth limited, iterative deepening, and bidirectional search • informed (Heuristic) search: search is guided by an evaluation function: Greedy best-first, A*, IDA*, and beam search • optimization in which the search is to find an optimal value of an objective ...
AI 1. Problem-solving agent • Four general steps in problem solving: • Goal formulation • What are the successful world states • Problem formulation • What actions and states to consider given the goal • Search • Determine the possible sequence of actions that lead to the states of known values and then choosing the best sequence.
Artificial Intelligence: A Modern Approach by Stuart Russell and Peter Norvig Lecture Slides . Introduction to Artificial Intelligence (State-of-Art PPT file) Problem Solving and Uninformed Search; Heuristic Search; Game Playing; Knowledge Representation, Reasoning, and Propositional Logic; First-Order Predicate Logic; Logical Inference Methods
Artificial Intelligence Solving problems by searching. Fall 2008 professor: Luigi Ceccaroni. Problem solving. We want: To automatically solve a problem We need: A representation of the problem Algorithms that use some strategy to solve the problem defined in that representation.
PowerPoint presentations on AI can delve into various topics such as machine learning, neural networks, expert systems, and genetic algorithms. Problem solving is a fundamental aspect of artificial intelligence. AI algorithms and techniques are designed to tackle complex problems and find optimal solutions.
Explore the power of problem solving in artificial intelligence with this informative PowerPoint presentation, covering key concepts and techniques for tackling complex challenges effectively.
1. The document discusses problem solving and search in artificial intelligence. It defines what a problem is and describes how many problems can be solved through search by exploring alternatives in a search space.
Artificial intelligence (AI) problem-solving often involves investigating potential solutions to problems through reasoning techniques, making use of polynomial and differential equations, and carrying them out and use modelling frameworks. A same issue has a number of solutions, that are all accomplished using an unique algorithm.
Artificial Intelligence 3. Search in Problem Solving. Course V231 Department of Computing Imperial College, London Jeremy Gow. Problem Solving Agents. Looking to satisfy some goal Wants environment to be in particular state Have a number of possible actions An action changes environment...
FHFA Generative AI in Housing Finance TechSprint: Problem Statements Umbrella Stateme nt Generative artificial intelligence (AI) has captured the imagination and interest of a diverse set of stakeholders, including industry, government, and consumers.
Problem solving Problem formulation Search Techniques for Artificial Intelligence Classification of AI searching Strategies What is Search strategy ?
To help train the artificial-intelligence model to produce the desired results, the agency hosted trainings on how to use Lucy and encouraged everyone to use it and provide feedback.