CS541 Review Jim Blythe
2 Planning for the Grid USC INFORMATION SCIENCES INSTITUTE
LIGO’s Pulsar Search (Laser Interferometer Gravitational-wave Observatory) I nterferom archive eter Short Extract Fourier transpose channel Transform Long tim e fram es raw channels 3 0 m inutes Short tim e fram es Single Fram e Tim e- frequency I m age Extract Hz frequency Construct Find Candidate event range image DB Store USC INFORMATION SCIENCES INSTITUTE 3 Time
Operators include data dependencies, host and resource constraints. ( operator pulsar-search ( preconds ((<host> (or Condor-pool Mpi)) ( effects (<start-time> Number) () (<channel> Channel) ( (<fcenter> Number) (add (created <file>)) (<right-ascension> Number) (add (at <file> <host>)) (<sample-rate> Number) (add (pulsar <start-time> <end-time> <channel> (<file> File-Handle) <instrument> <format> ;; These two are parameters for the frequency-extract. <fcenter> <fband> (<f0> (and Number (get-low-freq-from-center-and-band <fderv1> <fderv2> <fderv3> <fderv4> <fderv5> <fcenter> <fband>))) <right-ascension> <declination> <sample-rate> (<fN> (and Number (get-high-freq-from-center-and-band <file>)) <fcenter> <fband>))) ) (<run-time> (and Number )) (estimate-pulsar-search-run-time <start-time> <end-time> <sample-rate> <f0> <fN> <host> <run-time>))) …) (and (available pulsar-search <host>) (forall ((<sub-sft-file-group> (and File-Group-Handle (gen-sub-sft-range-for-pulsar-search <f0> <fN> <start-time> <end-time> <sub-sft-file-group>)))) (and (sub-sft-group <start-time> <end-time> <channel> <instrument> <format> <f0> <fN> <sample-rate> <sub-sft-file-group>) (at <sub-sft-file-group> <host>))))) USC INFORMATION SCIENCES INSTITUTE 4
High-level specs of desired results and intermediate data products Metadata Catalog Service Request Manager Workflow Globus Replica Planning Location Service AI-based Current Models and State Planner current state Generator information Globus Monitoring and Discovery Service Submission and Monitoring System information Resource Models Concrete Workflow Dynamic Monitoring information workflow executor Execution Information and (DAGman) Models tasks Grid Grid Grid Raw data detector USC INFORMATION SCIENCES INSTITUTE 5
Temporal logics for planning USC INFORMATION SCIENCES INSTITUTE 6
7 Fahiem Bacchus USC INFORMATION SCIENCES INSTITUTE
8 Fahiem Bacchus USC INFORMATION SCIENCES INSTITUTE
Heuristic search planning USC INFORMATION SCIENCES INSTITUTE 9
Derive cost estimate from a relaxed planning problem � Ignore the deletes on actions � BUT – still NP-hard, so approximate: � For individual propositions p: d(s, p) = 0 if p is true in s = 1 + min(d(s, pre(a))) otherwise [min over actions a that add p] USC INFORMATION SCIENCES INSTITUTE 10
HSP2 overview � Best-first search, using h+ � Based on WA* - weighted A*: f(n) = g(n) + W * h(n). If W = 1, it’s A* (with admissible h). If W > 1, it’s a little greedy – generally finds solutions faster, but not optimal. � In HSP2, W = 5 USC INFORMATION SCIENCES INSTITUTE 11
HSPr problem space � States are sets of atoms (correspond to sets of states in original space) � initial state is the goal G � Goal states are those that are true in s0 (initial state in planning problem) � Still use h+. h+(s) = sum g(s0, p) USC INFORMATION SCIENCES INSTITUTE 12
Mutexes in HSPr, take 2 � Better definition: A set M of pairs R = {p, q} is a mutex set if (1) R is not true in s0 (2) for every op o that adds p, either o deletes q or o does not add q, and for some precond r of o, {r, q} is in M. Recursive definition allows for some interaction of the operators USC INFORMATION SCIENCES INSTITUTE 13
Temporal reasoning and scheduling USC INFORMATION SCIENCES INSTITUTE 14
Temporal planning with mutual exclusion relation � Propositions and actions are monotonically increasing, no-goods monotonically decreasing: USC INFORMATION SCIENCES INSTITUTE 15
ASPEN � Combine planning and scheduling steps as alternative ‘conflict repair’ operations � Activities have start time, end time, duration � Maintain ‘most-commitment’ approach – easier to reason about temporal dependencies with full information � C.f. TLPlan USC INFORMATION SCIENCES INSTITUTE 16
Contributors for a non-depletable resource violation USC INFORMATION SCIENCES INSTITUTE 17
Contributors for a depletable resource violation USC INFORMATION SCIENCES INSTITUTE 18
Learning search control knowledge and case-based planning USC INFORMATION SCIENCES INSTITUTE 19
Using EBL to improve plan quality � Given: planning domain, evaluation function planner’s plan, a better plan � Learn: control knowledge to produce the better plan � Explanation used: explain why the alternative plan is better � Target concept: control rules that make choices based on the planner state and meta-state USC INFORMATION SCIENCES INSTITUTE 20
Architecture of Quality system USC INFORMATION SCIENCES INSTITUTE 21
Explaining better plans recursively: target concept: shared subgoal USC INFORMATION SCIENCES INSTITUTE 22
Hamlet: blame assignment USC INFORMATION SCIENCES INSTITUTE 23
24 Probabilistic planning USC INFORMATION SCIENCES INSTITUTE
Sources of uncertainty � Incomplete knowledge of the world (uncertain initial state) � Non-deterministic effects of actions � Effects of external agents or state dynamics. USC INFORMATION SCIENCES INSTITUTE 25
Dealing with uncertainty: re-planning and conditional planning � Re-planning: � Make a plan assuming nothing bad will happen � Build a new plan if a problem is found � (either re-plan to the goal state or try to repair the plan) � In some cases, this is too late. � Deal with contingencies (plans for bad outcomes) at planning time, before they occur. � Can’t plan for every contingency, so need to prioritize � Implies sensing � Build a plan that reduces the number of contingencies requires (conformant planning) � May not be possible USC INFORMATION SCIENCES INSTITUTE 26
A Buridan plan based on SNLP USC INFORMATION SCIENCES INSTITUTE 27
Computing the probability of success 2: Bayes nets Time-stamped literal node Action outcome node What is the worst-case time complexity of this algorithm? USC INFORMATION SCIENCES INSTITUTE 28
MAXPLAN � Inspired by SATPLAN. Compile planning problem to an instance of E-MAJSAT � E-MAJSAT: given a boolean formula with variables that are either choice variables or chance variables, find an assignment to the choice variables that maximizes the probability that the formula is true. � Choice variables: we can control them � e.g. which action to use � Chance variables: we cannot control them � e.g. the weather, the outcome of each action, .. � Then use standard algorithm to compute and maximize probability of success USC INFORMATION SCIENCES INSTITUTE 29
Probabilistic planning: exogenous events USC INFORMATION SCIENCES INSTITUTE 30
Representing external sources of change Model actions that external agents can take in the same way as actions that the planner can take. ( event oil-spills (probability 0.1) (preconds (and (oil-in-tanker <sea-sector>) (poor-weather <sea-sector>))) (effects (del (oil-in-tanker <sea-sector>)) (add (oil-in-sea <sea-sector>)))) USC INFORMATION SCIENCES INSTITUTE 31
Computing the probability of success using a Bayes net USC INFORMATION SCIENCES INSTITUTE 32
Example: the weather events and the corresponding markov chain � The markov chain shows possible states independent of time. � As long as transition probabilities are independent of time, the probability of the state at some future time t can be computed in logarithmic time complexity in t. � The computation time is polynomial in the number of states in the markov chain. USC INFORMATION SCIENCES INSTITUTE 33
The event graph � Captures the dependencies between events needed to build small but correct markov chains. � Any event whose literals should be included will be an ancestor of the events governing objective literals. USC INFORMATION SCIENCES INSTITUTE 34
Probabilistic planning: structured policy iteration USC INFORMATION SCIENCES INSTITUTE 35
Craig Boutilier Structured representation � States decomposable into state variables � Structured representations the norm in AI � STRIPS, Sit-Calc., Bayesian networks, etc. � Describe how actions affect/depend on features � Natural, concise, can be exploited computationally � Same ideas can be used for MDPs � actions, rewards, policies, value functions, etc. � dynamic Bayes nets [DeanKanazawa89,BouDeaGol95] � decision trees and diagrams [BouDeaGol95,Hoeyetal99] USC INFORMATION SCIENCES INSTITUTE 36
37 Craig Boutilier Action Representation – DBN/ADD USC INFORMATION SCIENCES INSTITUTE
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