Upper-Expectile Multi-Step Q-Learning for Off-Policy Reinforcement Learning

Multi-step returns accelerate reward propagation in off-policy reinforcement learning, but couple the evaluation of each decision to the suboptimal logged actions that follow it, inducing a pessimistic bias that grows with the horizon. We propose Expectile $n$-step Q-learning (ENQ), which replaces the symmetric $n$-step temporal-difference (TD) loss with an asymmetric expectile loss on the action-value error, with expectile level $τ$ as the only method-specific hyperparameter added beyond $n$-step TD. We prove that the ENQ operator is a $γ^{n}$-contraction. Under deterministic dynamics, at $τ=1$, its bias vanishes at the optimal action-value function $Q^*$ on covered in-support pairs, and the corresponding fixed point satisfies the separation-$n$ instance and its multiples of the lower-bound inequality used by Long-Horizon Q-learning (LQL). Under stochastic dynamics, the operator bias admits two-sided bounds with horizon-independent noise constants. Using a single expectile level $τ=0.8$ and a fixed backup horizon across 27 manipulation and navigation task instances, ENQ is competitive with LQL on aggregate, achieves higher measured training-step throughput in our profiling study, and benefits more from a ten-critic ensemble in a controlled scaling experiment.

Entropy-Regularized Adjoint Matching for Offline RL

Integrating expressive generative policies, such as flow-matching models, into offline reinforcement learning (RL) allows agents to capture complex, multi-modal behaviors. While Q-learning with Adjoint Matching (QAM) stabilizes policy optimization via the continuous adjoint method, it remains inherently bound to the fixed behavior distribution. This dependence induces a \textit{popularity bias} that can suppress high-reward actions in low-density regions, and creates a \textit{support binding} that restricts off-manifold exploration. Existing workarounds, such as appending \textit{residual} Gaussian policies, often re-introduce the expressivity bottlenecks associated with unimodal distributions. In this work, we propose \textit{Maximum Entropy Adjoint Matching} (ME-AM), a unified framework that addresses these limitations within the continuous flow formulation. ME-AM incorporates two mechanisms: (1) a Mirror Descent entropy maximization objective that mitigates the popularity bias to facilitate the extraction of optimal policies from offline datasets, and (2) a \textit{Mixture Behavior Prior} that mathematically broadens the geometric support to encompass out-of-distribution high-reward regions. By exploring this extended geometry, ME-AM identifies robust actions while preserving the absolute continuity of the generative vector field. Empirically, ME-AM demonstrates competitive or superior performance compared to prior state-of-the-art (SOTA) methods across a diverse suite of sparse-reward continuous control environments.

Multi-Objective Decision Transformers for Offline Reinforcement Learning

Offline Reinforcement Learning (RL) is structured to derive policies from static trajectory data without requiring real-time environment interactions. Recent studies have shown the feasibility of framing offline RL as a sequence modeling task, where the sole aim is to predict actions based on prior context using the transformer architecture. However, the limitation of this single task learning approach is its potential to undermine the transformer model's attention mechanism, which should ideally allocate varying attention weights across different tokens in the input context for optimal prediction. To address this, we reformulate offline RL as a multi-objective optimization problem, where the prediction is extended to states and returns. We also highlight a potential flaw in the trajectory representation used for sequence modeling, which could generate inaccuracies when modeling the state and return distributions. This is due to the non-smoothness of the action distribution within the trajectory dictated by the behavioral policy. To mitigate this issue, we introduce action space regions to the trajectory representation. Our experiments on D4RL benchmark locomotion tasks reveal that our propositions allow for more effective utilization of the attention mechanism in the transformer model, resulting in performance that either matches or outperforms current state-of-the art methods.