FedQHD: Closed-Form Function-Space Federated Reinforcement Learning

Federated reinforcement learning enables decentralized agents to collaboratively improve policies or value estimates without exchanging raw trajectories. However, FedAvg-style parameter averaging is not function-space consistent: when clients use heterogeneous encoders or even identical nonlinear networks, averaged parameters need not correspond to the weighted average of client value functions in any common function space. We propose FedQHD, a federated Q-learning method using hyperdimensional (random-feature) state encoders with a linear readout, so that Q-functions are nonlinear in state yet linear in trainable parameters. This linear structure enables closed-form aggregation. With a shared encoder, the function-space consensus update coincides exactly with weighted averaging of local readout matrices. With heterogeneous encoders, the server constructs a global teacher by averaging client Q-values on a shared anchor-state set, and each client compiles this teacher into its local representation via a single ridge projection. We formalize the federation gap -- the error incurred when compiling a federated teacher into a heterogeneous client representation -- relative to a client-specific oracle projection. We show that this gap decomposes into subspace misalignment, anchor-set conditioning, and regularization bias. We further identify the anchor-to-dimension ratio $m \geq D_i$ as the well-conditioned regime in which the gap reduces to a multiple of the encoder heterogeneity floor. On four continuous-state, discrete-action control benchmarks, FedQHD matches or outperforms FedAvg-style baselines and distillation-based alternatives while requiring substantially less computation, and the empirical dependence of the federation gap on encoder dimension matches our theoretical analysis.

Online Learning and Equilibrium Computation with Ranking Feedback

Online learning in arbitrary, and possibly adversarial, environments has been extensively studied in sequential decision-making, and it is closely connected to equilibrium computation in game theory. Most existing online learning algorithms rely on \emph{numeric} utility feedback from the environment, which may be unavailable in human-in-the-loop applications and/or may be restricted by privacy concerns. In this paper, we study an online learning model in which the learner only observes a \emph{ranking} over a set of proposed actions at each timestep. We consider two ranking mechanisms: rankings induced by the \emph{instantaneous} utility at the current timestep, and rankings induced by the \emph{time-average} utility up to the current timestep, under both \emph{full-information} and \emph{bandit} feedback settings. Using the standard external-regret metric, we show that sublinear regret is impossible with instantaneous-utility ranking feedback in general. Moreover, when the ranking model is relatively deterministic, \emph{i.e.}, under the Plackett-Luce model with a temperature that is sufficiently small, sublinear regret is also impossible with time-average utility ranking feedback. We then develop new algorithms that achieve sublinear regret under the additional assumption that the utility sequence has sublinear total variation. Notably, for full-information time-average utility ranking feedback, this additional assumption can be removed. As a consequence, when all players in a normal-form game follow our algorithms, repeated play yields an approximate coarse correlated equilibrium. We also demonstrate the effectiveness of our algorithms in an online large-language-model routing task.

Mutual Theory of Mind in Human-AI Collaboration: An Empirical Study with LLM-driven AI Agents in a Real-time Shared Workspace Task

Theory of Mind (ToM) significantly impacts human collaboration and communication as a crucial capability to understand others. When AI agents with ToM capability collaborate with humans, Mutual Theory of Mind (MToM) arises in such human-AI teams (HATs). The MToM process, which involves interactive communication and ToM-based strategy adjustment, affects the team's performance and collaboration process. To explore the MToM process, we conducted a mixed-design experiment using a large language model-driven AI agent with ToM and communication modules in a real-time shared-workspace task. We find that the agent's ToM capability does not significantly impact team performance but enhances human understanding of the agent and the feeling of being understood. Most participants in our study believe verbal communication increases human burden, and the results show that bidirectional communication leads to lower HAT performance. We discuss the results' implications for designing AI agents that collaborate with humans in real-time shared workspace tasks.