1. Stuart Russell and Jason Wolfe UC Berkeley
Kriegspiel
Stuart Russell and Jason Wolfe
UC Berkeley
From Efficient belief-state AND–OR search, with application to Kriegspiel.
IJCAI 2005 (in press).
UCB 5/18/2005

2. The Real World… Contains multiple agents with disparate goals
Requires adversarial decision making
Commonly studied through fully observable games, such as chess or backgammon
Is partially observable
Agents must make decisions, despite having incomplete knowledge about the state of their environment
Agents should consider both their own information state (to gather information) and their opponent’s information state (to hide information)
Optimal strategies are randomized
Can thus be modeled by partially observable games (e.g., poker)
UCB 5/18/2005

3. Kriegspiel (“war-game”)
A partially observable variant of chess – opponent pieces invisible, moves secret
Referee observes actions, provides percepts
Players attempt possibly-legal actions until one is legal
Symmetric player percepts
Move illegal; repeated identical illegal moves disallowed; attempts (except pawn captures) must be legal in absence of opponent pieces
Capture occurred on <square>
Check occurred in <directions>. <directions> is one or more of Rank, File, Long Diagonal, Short Diagonal, or Knight (from king’s perspective)
Checkmate and stalemate
UCB 5/18/2005

4. Task/Metric
Task: given a Kriegspiel move and observation history for White, determine if White can guarantee a win within 3-ply (actual moves)
Can assume that Black has full observation, consider only deterministic strategies
Two sub-problems
State estimation: determine belief state, set of possible board positions consistent with move and observation history
Move selection: given the belief state, determine a move plan for White that guarantees a win within 3-ply
Metric: performance on a Kriegspiel checkmate problem database
By playing two different Kriegspiel agents, generated database of 500 “mate instances” with guaranteed wins for White and 500 “near-miss instances” that “almost” have guaranteed wins for White.
Measure accuracy in classifying database problem instances as mates/near-misses within some fixed time limit
UCB 5/18/2005

5. Belief-State AND–OR Search
Test for guaranteed checkmate by searching a tree whose nodes correspond to White’s belief states
Common algorithms are depth-first search (DFS) and proof-number search (PNS)
Both treat a belief state as a “black box”
UCB 5/18/2005

6. Algorithmic Contribution
Mate Instance Solve Time
Developed a new family of “incremental” belief-state AND–OR search algorithms that “look inside” the belief state
Treat uncertainty as a new search dimension in addition to familiar depth and breadth
G-DBU and IPNS (black and blue at right) are two incremental algorithms
Both can be orders of magnitude faster than previous algorithms
Near-Miss Instance Solve Time
UCB 5/18/2005

7. New algorithms can solve 3-ply database instances with 98% accuracy in 10 s.
UCB 5/18/2005

8. Demonstrations Demo 1: state estimation for a 3-ply mate instance
Demo 2: move selection for this same problem instance
Demo 3: play against our Kriegspiel agent
UCB 5/18/2005