CAP-DO: Learned Contextual Action Proposals for Certified Double-Oracle Solving Across Related Zero-Sum Games

Abstract

Many security and inspection-planning problems require solving a sequence of related zero-sum games. Across this sequence, the feasible defender and attacker action spaces re-main fixed, whereas each context induces a different payoff matrix through changes in target values, inspection effective-ness, costs, and interaction effects. Double Oracle (DO) solves large zero-sum games without materializing the full payoff matrix by iteratively expanding a restricted game. However, applying standard DO independently to each new payoff context requires restarting the search from a generic restricted game and requires rediscovering context-relevant actions through full-space best responses. We propose Con-textual Action Proposal Double Oracle (CAP-DO), a learning-augmented framework that warm-starts DO for repeated contextual games. Offline, CAP-DO trains separate defender and attacker rankers once from solved contexts. Online, the fixed rankers propose initial restricted action sets for each new context. Learning therefore determines where certified search starts, while the current game, through full-space best-response checks and a two-sided certificate, still determines whether the output is accepted. Theoretically, CAP-DO pre-serves DO's full-game certification guarantee, so every accepted output meets the prescribed certificate tolerance. Under standard exact-oracle assumptions, CAP-DO also retains finite convergence when expansion is uncapped. Empirically, across three scales of a non-additive contextual inspection-game benchmark, with up to 9,880 actions per player, CAP-DO-balanced achieves higher certification rates and uses few-er full-space best-response calls than cold-start, trace-reuse, and heuristic warm starts under fixed expansion budgets.