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) state  action 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