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Safe and Robust Subgame Exploitation in Imperfect Information Games
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Proposes adaptation safety (exploitation strategy no more exploitable than the blueprint) and OX-Search, a real-time subgame search with a gadget game for safe, robust opponent exploitation in imperfect-information poker.
Problem
Opponent exploitation in two-player zero-sum imperfect-information games is vulnerable to opponent modeling errors and deceptive adversaries, and traditional NE-based safety is overly strict for large games where strategies are inherently exploitable.
Approach
Defines adaptation safety (exploitability must not exceed that of the blueprint) and formulates subgame exploitation as maximizing estimated opponent-reach-weighted improvement subject to per-infoset counterfactual safety constraints, solved via a gadget game with CFR so that no exploitation level hyperparameter is needed.
Key results
- OX-Search has lower exploitability than the blueprint in Leduc Hold'em and Flop Hold'em Poker and is insensitive to increasing estimation error, while RNR's exploitability rises with error.
- Against evolving opponents, OX-Search consistently outperforms Real-time RNR, SES and the blueprint in both games.
- In Flop Hold'em Poker with modeling errors, OX-Search outperforms both SES and RNR; in Leduc it is comparable to SES.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace the blueprint strategy with OX-Search | Opponent exploitation in Leduc Hold’em and Flop Hold’em Poker · Leduc Hold’em and Flop Hold’em Poker | exploitability | Helped |
| use OX-Search as modeling error increases | Opponent exploitation in Leduc Hold’em and Flop Hold’em Poker · Leduc Hold’em and Flop Hold’em Poker | exploitability | No clear effect |
| replace Real-time RNR or SES with OX-Search | Opponent exploitation against evolving opponents · Leduc Hold’em and Flop Hold’em Poker | evaluation | Helped |
| replace SES with OX-Search | Opponent exploitation under modeling errors · Leduc Hold’em | evaluation | No clear effect |
| replace SES or RNR with OX-Search | Opponent exploitation under modeling errors · Flop Hold’em Poker | evaluation | Helped |
| use SES instead of the blueprint strategy | Opponent exploitation · Leduc Hold’em | exploitability | No clear effect |
| use SES instead of the blueprint strategy | Opponent exploitation · Flop Hold’em Poker | exploitability | Helped |
| use Real-time RNR as modeling error increases | Opponent exploitation · Leduc Hold’em and Flop Hold’em Poker | exploitability | Hurt |
| use OX-Search instead of other exploitation methods | Opponent exploitation against evolving opponents · Leduc Hold’em and Flop Hold’em Poker | evaluation | Helped |
Surprising findings
- SES reduced exploitability in Flop Hold'em but was less effective in Leduc Hold'em, attributed to abstraction differences.
Limitations
- Framework uses only opponent reach probabilities and does not model predictions of opponent future actions.
- Requires choosing or increasing the Lagrange bound beta; safety violation may occur if optimal multipliers fall outside the bound.
- Evaluated only on poker games (Leduc and Flop Hold'em) with synthetic opponents.
Experimental setup
Datasets: Leduc Hold'em Flop Hold'em Poker
Benchmarks: Leduc Hold'em Flop Hold'em Poker
Metrics: exploitability (mbb/h) head-to-head evaluation (mbb/h)
Baselines: Blueprint Real-time RNR SES
Builds on: safe subgame solving Constrained CFR Restricted Nash Response Safe Exploitation Search
Closest papers by meaning
- Opponent-Model Search in Games with Incomplete Information (AAAI 2024 · similarity 0.86)
- The Update-Equivalence Framework for Decision-Time Planning (ICLR 2024 · similarity 0.86)
- The Attacker in the Mirror: Breaking Self-Consistency in Safety via Anchored Bipolicy Self-Play (NeurIPS 2026 · similarity 0.85)
- Preference-CFR: Beyond Nash Equilibrium for Better Game Strategies (ICML 2025 · similarity 0.84)
- Securing Equal Share: A Principled Approach for Learning Multiplayer Symmetric Games (ICML 2025 · similarity 0.84)
- Fast Peer Adaptation with Context-aware Exploration (ICML 2024 · similarity 0.84)
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