Model-based Reflex Agents: Handling Infinite Sequences & Utility Planning

1. 8/27 Current make-up: 13 UG; 21 G; +~3 Assignment 0 due next Wednesday 9/5

2. Review

3. (Model-based reflex agents)

4. Even basic survival needs state information.. This one already assumes that the “sensorsfeatures” mapping has been done!

5. (aka Model-based Reflex Agents) EXPLICIT MODELS OF THE ENVIRONMENT --Blackbox models (child function) --Logical models --Probabilistic models Representation & Reasoning

6. It is not always obvious what action to do now given a set of goals You woke up in the morning. You want to attend a class. What should your action be?  Search (Find a path from the current state to goal state; execute the first op) Planning (does the same for logical—non-blackbox state models)

7. ..certain inalienable rights—life, liberty and pursuit of ?Money ?Daytime TV ?Happiness (utility) --Decision Theoretic Planning --Sequential Decision Problems

8. Discounting • The decision-theoretic agent often needs to assess the utility of sequences of states (also called behaviors). • One technical problem is “How do keep the utility of an infinite sequence finite? • A closely related real problem is how do we combine the utility of a future state with that of a current state (how does 15$ tomorrow compare with 5000$ when you retire?) • The way both are handled is to have a discount factor r (0<r<1) and multiply the utility of nth state by rn • r0 U(so)+ r1 U(s1)+…….+ rn U(sn)+ • Guaranteed to converge since power series converge for 0<r<n • r is set by the individual agents based on how they think future rewards stack up to the current ones • An agent that expects to live longer may consider a larger r than one that expects to live shorter…

9. Representation Mechanisms: Logic (propositional; first order) Probabilistic logic Learning the models Search Blind, Informed Planning Inference Logical resolution Bayesian inference How the course topics stack up…

10. Learning Dimensions: What can be learned? --Any of the boxes representing the agent’s knowledge --action description, effect probabilities, causal relations in the world (and the probabilities of causation), utility models (sort of through credit assignment), sensor data interpretation models What feedback is available? --Supervised, unsupervised, “reinforcement” learning --Credit assignment problem What prior knowledge is available? -- “Tabularasa” (agent’s head is a blank slate) or pre-existing knowledge

11. Problem Solving Agents (Search-based Agents)

14. The important difference from the graph-search scenario you learned in CSE 310 is that you want to keep the graph implicit rather than explicit (i.e., generate only that part of the graph that is absolutely needed to get the optimal path)  VERY important since for most problems, the graphs are humongous..

15. “Factored Representation…”

17. What happens when the domain Is inaccessible?

18. 8/29 Blog seems alive and well Blog Czars appointed Will Cushing J. Benton Menkes van den Briel Kartik Talamadupula + Aravind (TA) Rao (instructor)

19. You search in this Space even if your Init state is known But actions are Non-deterministic Sensing reduces State Uncertainty Search in Multi-state (inaccessible) version Set of states is Called a “Belief State” So we are searching in the space of belief states

20. Utility of eyes (sensors) is reflected in the size of the effective search space! In general, a subgraph rather than a tree (loops may be needed consider closing a faulty door ) Given a state space of size n (or 2v where v is the # state variables) the single-state problem searches for a path in the graph of size n (2v) the multiple-state problem searches for a path in a graph of size 2n (22^v) the contingency problem searches for a sub-graph in a graph of size 2n (22^v) 2n is the EVILthat every CS student’s nightmares are made of

26. ?? General Search

28. Search algorithms differ based on the specific queuing function they use All search algorithms must do goal-test only when the node is picked up for expansion We typically analyze properties of search algorithms on uniform trees --with uniform branching factor b and goal depth d (tree itself may go to depth dt)

33. Breadth first search on a uniform tree of b=10 Assume 1000nodes expanded/sec 100bytes/node

35. Qn: Is there a way of getting linear memory search that is complete and optimal?

36. The search is “complete” now (since there is finite space to be explored). But still inoptimal.

38. IDDFS: Review

39. BFS: A,B,G A,B,C,D,G (A), (A, B, G) DFS: IDDFS: Note that IDDFS can do fewer Expansions than DFS on a graph Shaped search space. A B C D G

41. BFS: A,B,G A,B,A,B,A,B,A,B,A,B (A), (A, B, G) DFS: IDDFS: Note that IDDFS can do fewer Expansions than DFS on a graph Shaped search space. A B C D G Search on undirected graphs or directed graphs with cycles… Cycles galore…

42. Graph (instead of tree) Search: Handling repeated nodes Main points: --repeated expansions is a bigger issue for DFS than for BFS or IDDFS --Trying to remember all previously expanded nodes and comparing the new nodes with them is infeasible --Space becomes exponential --duplicate checking can also be exponential --Partial reduction in repeated expansion can be done by --Checking to see if any children of a node n have the same state as the parent of n -- Checking to see if any children of a node n have the same state as any ancestor of n (at most d ancestors for n—where d is the depth of n)

43. A A 1 0.1 Bait & Switch Graph N1:B(1) N2:G(9) B B 1 0.1 9 9 N3:C(2) C C 1 0.1 D N4:D(3) D 2 25 G G N5:G(5) Uniform Cost Search No:A (0) Completeness? Optimality? if d < d’, then paths with d distance explored before those with d’ Branch & Bound argument (as long as all op costs are +ve) Efficiency? (as bad as blind search..) Notation: C(n,n’) cost of the edge between n and n’ g(n) distance of n from root dist(n,n’’) shortest distance between n and n’’

44. Breadth-First goes level by level Visualizing Breadth-First & Uniform Cost Search This is also a proof of optimality…

45. Proof of Optimality of Uniform search Proof of optimality: Let N be the goal node we output. Suppose there is another goal node N’ We want to prove that g(N’) >= g(N) Suppose this is not true. i.e. g(N’) < g(N) --Assumption A1 When N was picked up for expansion, Either N’ itself, or some ancestor of N’, Say N’’ must have been on the search queue If we picked N instead of N’’ for expansion, It was because g(N) <= g(N’’) ---Fact f1 But g(N’) = g(N’’) + dist(N’’,N’) So g(N’) >= g(N’’) So from f1, we have g(N) <= g(N’) But this contradicts our assumption A1 No N’’ N N’ Holds only because dist(N’’,N’) >= 0 This will hold if every operator has +ve cost

46. A 0.1 Bait & Switch Graph N1:B(.1) N2:G(9) B 0.1 9 N3:C(.2) C 0.1 N4:D(.3) D 25 G N5:G(25.3) Admissibility Informedness “Informing” Uniform search… No:A (0) Would be nice if we could tell that N2 is better than N1 --Need to take not just the distance until now, but also distance to goal --Computing true distance to goal is as hard as the full search --So, try “bounds” h(n) prioritize nodes in terms of f(n) = g(n) +h(n) two bounds: h1(n) <= h*(n) <= h2(n) Which guarantees optimality? --h1(n) <= h2(n) <= h*(n) Which is better function?