4/22: scheduling (contd) planning with incomplete info (start)

4/22: Scheduling (contd)Planning with

incomplete info (start)

Earth which has many heights, and slopes and the unconfined plain that bind men together, Earth that bears plants of various healing powers, may she spread wide for us and thrive

-Bhoomi Sooktam Atharva Veda XII.I (~1500 B.C.)

Earth which has many heights, and slopes and the unconfined plain that bind men together, Earth that bears plants of various healing powers, may she spread wide for us and thrive

-Bhoomi Sooktam Atharva Veda XII.I (~1500 B.C.)

4/22: Scheduling (contd)Planning with

incomplete info (start)

Problems, Solutions, Success Measures:3 orthogonal dimensions

Incompleteness in the initial state Un (partial) observability of states Non-deterministic actions Uncertainty in state or effects Complex reward functions

(allowing degrees of satisfaction)

Conformant Plans: Don’t look—just do Sequences

Contingent/Conditional Plans: Look, and based on what you see, Do; look again Directed acyclic graphs

Policies: If in (belief) state S, do action a (belief) stateaction tables

Deterministic Success: Must reach goal-state with probability 1 Probabilistic Success: Must succeed with probability >= k

(0<=k<=1) Maximal Expected Reward: Maximize the expected reward (an

optimization problem)

Some specific cases

1.0 success conformant planning for domains with incomplete initial states

1.0 success conformant planning for domains with non-deterministic actions

1.0 success conditional plans for fully observable domains with incompletely specified init states, and deterministic actions

1.0 success conditional plans for fully observable domains with non-deterministic actions

1.0 success conditional plans for parially observable domains with non-deterministic actions

Probabilistic variants of all the ones on the left (where we want success probability to be >= k).

Paths to Perdition

Complexity of finding probability 1.0 success plans

Slides I missed: cgp slide Fragplan slides Dan bryce one slide Kacmbp slide The multiple init states vs. no sensing multiple init states the various approaches for Conformant planning the uncertainty reduction—why it may not always lead to goal state the point about belief states being propositional formulas The main slide about coulter.. Condeff vs. non-condeff Progression vs. regression get rid off geffner slides. Not all that useful anyway

Conformant Planning: Efficiency Issues

Belief states can get harder to manage The IRST group developed several techniques for representing and

manipulating belief states efficiently as BDDs (a canonical and compact representation for propositional formulae)

Significant speedup Graphplan (CGP) and SAT-compilation approaches have also

been tried for conformant planning Idea is to make plan in one world, and try to extend it as needed to make

it work in other worlds Planning graph based heuristics for conformant planning have

been investigated. Interesting issues involving multiple planning graphs

Deriving Heuristics? – relaxed plans that work in multiple graphs Compact representation? – Label graphs

KACMBP and Uncertainty reducing actions