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Artificial Intelligence Foundations Of Computational Agents 1st Edition David L. Poole, Alan K. Mackworth - Solutions

• Planning is the process of choosing a sequence of actions to achieve a goal.
• An agent can choose the best hypothesis given the training examples, delineate all of the hypotheses that are consistent with the data, or compute the posterior probability of the hypotheses given the training examples.
• Linear classifiers, decision trees, and Bayesian classifiers are all simple representations that are the basis for more sophisticated models.
• Given some training examples, an agent builds a representation that can be used for new predictions.
• Supervised learning is the problem that involves predicting the output of a new input, given a set of input–output pairs.
• Learning is the ability of an agent improve its behavior based on experience.
• A hidden Markov model or a dynamic belief network can be used for probabilistic reasoning in time, such as for localization.
• Stochastic simulation can be used for approximate inference.
• Exact inference can be carried out for sparse graphs (with low treewidth).
• A Bayesian belief network can be used to represent independence in a domain.
• The posterior probability is used to update an agent’s beliefs based on evidence.
• Probability can be used to make decisions under uncertainty.
• A causal model predicts the effect of an intervention.
• Abduction can be used to explain observations.
• Negation as failure can be used when the knowledge is complete (i.e., under the complete knowledge assumption).
• Proof by contradiction can be used to make inference from a Horn clause knowledge base.
• A sound and complete proof procedure can be used to determine the logical consequences of a knowledge base.
• Given a set of facts about a domain, the logical consequences characterize what else must be true.
• A definite clause knowledge base can be used to specify atomic clauses and rules about a domain when there is no uncertainty or ambiguity.
• Optimization can use systematic methods when the constraint graph is sparse. Local search can also be used, but the added problem exists of not knowing when the search is at a global optimum.
• Stochastic local search can be used to find satisfying assignments, but not to show there are no satisfying assignments. The efficiency depends on the trade-off between the time taken for each improvement and how much the value is improved at each step. Some method must be used to allow the
• Arc consistency and search can often be combined to find assignments that satisfy some constraints or to show that there is no assignment.
• Many problems can be represented as a set of variables, corresponding to the set of features, domains of possible values for the variables, and a set of hard and/or soft constraints. A solution is an assignment of a value to each variable that satisfies a set of hard constraints or optimizes
• Instead of reasoning explicitly in terms of states, it is almost always much more efficient for an agent solving realistic problems to reason in terms of a set of features that characterize a state.
• When graphs are small, dynamic programming can be used to record the actual cost of a least-cost path from each node to the goal, which can be used to find the next arc in an optimal path.
• Iterative deepening and depth-first branch-and-bound searches can be used to find least-cost paths with less memory than methods such as A∗, which store multiple paths.
• A∗ search can use a heuristic function that estimates the cost from a node to a goal. If this estimate underestimates the actual cost, A∗ is guaranteed to find a least-cost path first.
• Breadth-first and depth-first searches can find paths in graphs without any extra knowledge beyond the graph.
• Many problems can be abstracted as the problem of finding paths in graphs.
• An intelligent agent requires knowledge that is acquired at design time, offline or online.
• Complex agents are built modularly in terms of interacting hierarchical layers.
• An agent has direct access not to its history, but to what it has remembered(its belief state) and what it has just observed. At each point in time, an agent decides what to do and what to remember based on its belief state and its current observations.
• Agents are situated in time and must make decisions of what to do based on their history of interaction with the environment.
• An agent is composed of a body and interacting controllers.
• Agents have sensors and actuators to interact with the environment.
• An agent system is composed of an agent and an environment.
• In choosing a representation, you should find a representation that is as close as possible to the problem, so that it is easy to determine what it is representing and so it can be checked for correctness and be able to be maintained.Often, users want an explanation of why they should believe
• To know when you have solved a problem, an agent must have a definition of what constitutes an adequate solution, such as whether it has to be optimal, approximately optimal, or almost always optimal, or whether a satisficing solution is adequate.
• To solve a problem by computer, the computer must have an effective representation with which to reason.
• A designer of an intelligent agent should be concerned about modularity, how to describe the world, how far ahead to plan, uncertainty in both perception and the effects of actions, the structure of goals or preferences, other agents, how to learn from experience, and the fact that all real
• An intelligent agent is a physical symbol system that manipulates symbols to determine what to do.
• An agent acts in an environment and only has access to its prior knowledge, its history of observations, and its goals and preferences.
• Artificial intelligence is the study of computational agents that act intelligently.
Exercise 10.3 In the sequential prisoner’s dilemma (page 438), suppose there is a discount factor of γ, which means there is a probability γ of stopping at each stage. Is tit-for-tat a Nash equilibrium for all values of γ? If so, prove it. If not, for which values of γ is it a Nash
Exercise 10.2 In Example 10.12 (page 437), what is the Nash equilibrium with randomized strategies? What is the expected value for each agent in this equilibrium?
Exercise 10.1 For the hawk–dove game of Example 10.11 (page 436), where D > 0 and R > 0, each agent is trying to maximize its utility. Is there a Nash equilibrium with a randomized strategy? What are the probabilities? What is the expected payoff to each agent? (These should be expressed as
• By introducing payments, it is possible to design a mechanism that is dominant-strategy truthful and economically efficient.
• Agents can learn to coordinate by playing the same game repeatedly, but it is difficult to learn a randomized strategy.
• A Nash equilibrium is a strategy profile for each agent such that no agent can increase its utility by unilaterally deviating from the strategy profile.
• In partially observable domains, sometimes it is optimal to act stochastically.
• Perfect information games can be solved by backing up values in game trees or searching the game tree using minimax with α-β pruning.
• A multiagent decision network models probabilistic dependency and information availability.
• The extensive form of a game models agents’ actions and information through time in terms of game trees.
• The strategic form of a game specifies the expected outcome given controllers for each agent.
• A multiagent system consists of multiple agents who can act autonomously and have their own utility over outcomes. The outcomes depend on the actions of all agents. Agents can compete, cooperate, coordinate, communicate, and negotiate.
• The leaves represent final outcomes and are labeled with a utility for each agent.
• Each internal node labeled with nature has a probability distribution over its children.
• Each arc out of a node labeled with agent i corresponds to an action for agent i.
• Each internal node is labeled with an agent (or with nature). The agent is said to control the node.
Exercise 9.17 Consider a grid world where the action “up” has the following dynamics:That is, it goes up with probability 0.8, up-left with probability 0.1, and up-right with probability 0.1. Suppose we have the following states:s12 s13 s14 s17 s18 s19 There is a reward of +10 upon entering
Exercise 9.16 What is the main difference between asynchronous value iteration and standard value iteration? Why does asynchronous value iteration often work better than standard value iteration?
Exercise 9.15 Consider the following decision network:a) What are the initial factors. (You do not have to give the tables; just give what variables they depend on.)(b) Show what factors are created when optimizing the decision function and computing the expected value, for one of the legal
Exercise 9.14 One of the decisions we must make in real life is whether to accept an invitation even though we are not sure we can or want to go to an event. The following figure represents a decision network for such a problem:Suppose that all of the decision and random variables are Boolean
Exercise 9.13 This is a continuation of Exercise 6.8 (page 278).(a) When an alarm is observed, a decision is made whether to shut down the reactor. Shutting down the reactor has a cost cs associated with it (independent of whether the core was overheating), whereas not shutting down an overheated
Exercise 9.12 How can variable elimination for decision networks, shown in Figure 9.11 (page 393), be modified to include additive discounted rewards? That is, there can be multiple utility (reward) nodes, having to be added and discounted.Assume that the variables to be eliminated are eliminated
Exercise 9.11 In a decision network, suppose that there are multiple utility nodes, where the values must be added. This lets us represent a generalized additive utility function. How can the VE for decision networks algorithm, shown in Figure 9.11 (page 393), be altered to include such utilities?
Exercise 9.10 Consider a 5 × 5 grid game similar to the game of the previous question. The agent can be at one of the 25 locations, and there can be a treasure at one of the corners or no treasure.In this game the “up” action has dynamics given by the following diagram:That is, the agent goes
Exercise 9.9 Consider a game world:The robot can be at one of the 25 locations on the grid. There can be a treasure on one of the circles at the corners. When the robot reaches the corner where the treasure is, it collects a reward of 10, and the treasure disappears. When there is no treasure, at
Exercise 9.8 Explain why we often use discounting of future rewards in MDPs.How would an agent act differently if the discount factor was 0.6 as opposed to 0.9?
Exercise 9.7 Consider the belief network of Exercise 6.8 (page 278). When an alarm is observed, a decision is made whether to shut down the reactor. Shutting down the reactor has a cost cs associated with it (independent of whether the core was overheating), whereas not shutting down an overheated
Exercise 9.6 In Example 9.13 (page 389), suppose that the fire sensor was noisy in that it had a 20% false-positive rate, P(see smoke|report∧¬smoke) = 0.2, and a 15% false negative-rate:P(see smoke|report ∧ smoke) = 0.85.Is it still worthwhile to check for smoke?
Exercise 9.5 How sensitive are the answers from the decision network of Example 9.13 (page 389) to the probabilities? Test the program with different conditional probabilities and see what effect this has on the answers produced. Discuss the sensitivity both to the optimal policy and to the
Exercise 9.4 Suppose that, in a decision network, there were arcs from random variables “contaminated specimen” and “positive test” to the decision variable“discard sample.” Sally solved the decision network and discovered that there was a unique optimal policy:contaminated specimen
Exercise 9.3 Suppose that, in a decision network, the decision variable Run has parents Look and See. Suppose you are using VE to find an optimal policy and, after eliminating all of the other variables, you are left with the factor Look See Run Value true true yes 23 true true no 8 true false yes
Exercise 9.2 Consider the following decision network:This diagram models a decision about whether to cheat at two different time instances.Suppose P(watched) = 0.4, P(trouble1|cheat1, watched) = 0.8, and Trouble1 is true with probability 0 for the other cases. Suppose the conditional probability
Exercise 9.1 Students have to make decisions about how much to study for each course. The aim of this question is to investigate how to use decision networks to help them make such decisions.Suppose students first have to decide how much to study for the midterm.They can study a lot, study a
Exercise 8.15 The SNLP algorithm is the same as the partial-order planner presented here but, in the protect procedure, the condition is A = A0 and A = A1 and (A deletes G or A achieves G).This enforces systematicity, which means that for every linear plan there is a unique partial-ordered plan.
Exercise 8.14 The selection algorithm used in the partial-order planner is not very sophisticated. It may be sensible to order the selected subgoals. For example, in the robot world, the robot should try to achieve a carrying subgoal before an at subgoal because it may be sensible for the robot to
Exercise 8.13 To implement the function add constraint(A0 < A1, Constraints)used in the partial-order planner, you have to choose a representation for a partial ordering. Implement the following as different representations for a partial ordering:(a) Represent a partial ordering as a set of
Exercise 8.12 Give a condition for the CSP planner that, when arc consistency with search fails at some horizon, implies there can be no solutions for any longer horizon. [Hint: Think about a very long horizon where the forward search and the backward search do not influence each other.] Implement
Exercise 8.11 Explain how multiple-path pruning can be incorporated into a regression planner. When can a node be pruned?
Exercise 8.10 For the delivery robot domain, give a heuristic function for the regression planner that is non-zero and an underestimate of the actual path cost. Is it admissible?
Exercise 8.9 Explain how the regression planner can be extended to include maintenance goals, for either the feature-based representation of actions or the STRIPS representation. [Hint: Consider what happens when a maintenance goal mentions a feature that does not appear in a node.]
Exercise 8.8 In a forward planner, you can represent a state in terms of the sequence of actions that lead to that state.(a) Explain how to check if the precondition of an action is satisfied, given such a representation.(b) Explain how to do cycle detection in such a representation. You can assume
Exercise 8.7 Suppose you have a STRIPS representation for actions a1 and a2, and you want to define the STRIPS representation for the composite action a1; a2, which means that you do a1 then do a2.(a) What is the effects list for this composite action?(b) What are the preconditions for this
Exercise 8.6 Suggest a good heuristic for a forward planner to use in the robot delivery domain. Implement it. How well does it work?
Exercise 8.5 Suppose we must solve planning problems for cleaning a house.Various rooms can be dusted (making the room dust-free) or swept (making the room have a clean floor), but the robot can only sweep or dust a room if it is in that room. Sweeping causes a room to become dusty (i.e., not
Exercise 8.3 Write a complete description of the limited robot delivery world, and then draw a state-space representation that includes at least two instances of each of the blocks-world actions discussed in this chapter. Notice that the number of different arcs depends on the number of instances
Exercise 8.2 Suppose the robot cannot carry both coffee and mail at the same time. Give two different ways that the CSP that represents the planning problem can be changed to reflect this constraint. Test it by giving a problem where the answer is different when the robot has this limitation than
Exercise 8.1 Consider the planning domain in Figure 8.1 (page 350).(a) Give the feature-based representation of the MW and RHM features.(b) Give the STRIPS representations for the pick up mail and deliver mail actions.
Exercise 7.17 Implement a nearest-neighbor learning system that stores the training examples in a kd-tree and uses the neighbors that differ in the fewest number of features, weighted evenly. How well does this work in practice?
Exercise 7.16(a) Draw a kd-tree for the data of Figure 7.1 (page 289). The topmost feature to split on should be the one that most divides the examples into two equal classes. Assume that you know that the UserAction feature does not appear in subsequent queries, and so it should not be split on.
Exercise 7.15 In the neural net learning algorithm, the parameters are updated for each example. To compute the derivative accurately, the parameters should be updated only after all examples have been seen. Implement such a learning algorithm and compare it to the incremental algorithm, with
Exercise 7.14 Run the AIspace.org neural network learner on the data of Figure 7.1 (page 289).(a) Suppose that you decide to use any predicted value from the neural network greater than 0.5 as true, and any value less than 0.5 as false. How many examples are misclassified initially? How many
Exercise 7.13 Give an example where a naive Bayesian classifier can give inconsistent results when using empirical frequencies as probabilities. [Hint: You require two features, say A and B, and a binary classification, say C, that has domain{0, 1}. Construct a data set where the empirical
Exercise 7.12 Show how gradient descent can be used for learning a linear function that minimizes the absolute error. [Hint: Do a case analysis of the error. The error is differentiable at every point except when the error is zero, in which case it does not need to be updated.]
Exercise 7.11 As outlined in Example 7.18 (page 322), define a code for describing decision trees. Make sure that each code corresponds to a decision tree (for every sufficiently long sequence of bits, the initial segment of the sequence will describe a unique decision tree), and each decision tree
Exercise 7.10 In choosing which feature to split on in decision-tree search, an alternative heuristic to the max information split of Section 7.3.1 is to use the Gini index.The Gini index of a set of examples (with respect to target feature Y) is a measure of the impurity of the
Exercise 7.9 The decision-tree learning algorithm of Figure 7.5 (page 300) has to stop if it runs out of features and not all examples agree.Suppose that you are building a decision tree and you have come to the stage where there are no remaining features to split on and there are examples in the
Exercise 7.8 Extend the decision-tree learning algorithm of Figure 7.5 (page 300)so that multivalued features can be represented. Make it so that the rule form of the decision tree is returned.One problem that must be overcome is when no examples correspond to one particular value of a chosen

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