Junyan Liu, Haipeng Luo, Lillian J. Ratliff, Zihan Zhang
We study online learning in two-player uninformed Markov games, where the opponent may follow an arbitrary, unknown policy in each episode and the learner does not observe the opponent's actions. [TWYS21] showed that achieving sublinear external regret requires an exponential dependence on the episode length $H$. Motivated by this limitation, they studied the weaker notion of Nash-value regret and obtained an $\widetilde{O}(K^{2/3})$ regret bound, where $K$ is the number of episodes. More recently, [LLZR26] introduced a stronger notion called empirical Nash-value regret and achieved an $\widetilde{O}(\sqrt{K})$ bound when the opponent's non-stationarity is moderate, including the case where the opponent follows a fixed policy. However, whether the $\sqrt{K}$ rate is achievable in the worst case remained open. In this paper, we resolve this open question by developing an algorithm that achieves $\widetilde{O}(H^{3/2}S\sqrt{AK})$ empirical Nash-value regret against arbitrary opponent policies, where $S$ is the number of states and $A$ is the number of learner's actions. Specifically, our algorithm combines global and local planning by maintaining a collection of candidate predictions of future losses, each associated with a policy. Global planning learns which candidates to favor across episodes, while local planning combines their policies differently at each state to make decisions. A key ingredient is to coordinate these two components to control the discrepancy between local loss estimates and the total loss of the executed policy, using only the learner's observed trajectories.
Chenxiao Fan, Chongming Gao, Gangyi Zhang, Yaxin Gong, Leyang Shen, Jiakai Wang, Dong Wang, Yang Liu 等 12 位作者
Complex information seeking on the Web often requires collecting evidence from multiple documents and reasoning across them, as in multi-hop question answering. Multi-agent systems address such tasks by dividing work among specialized agents, where upstream agents produce intermediate answers and supporting evidence that downstream agents build upon. However, upstream answers vary in correctness, and most systems provide no quantitative signal about it, leaving the downstream agent to judge whether to trust or verify what it receives based solely on the textual evidence. In this paper, we propose MASCAL. Each agent learns to produce a correctness probability for its answer by jointly optimizing task performance and confidence calibration in reinforcement learning; the upstream agent passes this probability at handoff, giving the downstream agent a quantitative basis for its decisions, and the final answer also carries a calibrated probability, quantifying the reliability of the system output. To guide the downstream agent in using this signal during training, we introduce confidence-aware weighting, which increases the learning weight at positions responsive to the upstream probability, so that the agent learns more from decisions where it actively uses the signal. Across three collaboration architectures spanning Web retrieval and reasoning tasks, MASCAL improves task accuracy and calibration quality for both agents, and generalizes to deeper collaboration chains and different model scales. Intervention analysis confirms that upstream confidence affects downstream decision behavior, and the learned final confidence supports selective answering and targeted rechecking.