Vector-Valued Distributional Reinforcement Learning Policy Evaluation: A Hilbert Space Embedding Approach

We propose an (offline) multi-dimensional distributional reinforcement learning framework (KE-DRL) that leverages Hilbert space mappings to estimate the kernel mean embedding of the multi-dimensional value distribution under a proposed target policy. In our setting, the state-action variables are multi-dimensional and continuous. By mapping probability measures into a reproducing kernel Hilbert space via kernel mean embeddings, our method replaces Wasserstein metrics with an integral probability metric. This enables efficient estimation in multi-dimensional state-action spaces and reward settings, where direct computation of Wasserstein distances is computationally challenging. Theoretically, we establish contraction properties of the distributional Bellman operator under our proposed metric involving the Matern family of kernels and provide uniform convergence guarantees. Simulations and empirical results demonstrate robust off-policy evaluation and recovery of the kernel mean embedding under mild assumptions, namely, Lipschitz continuity and boundedness of the kernels, highlighting the potential of embedding-based approaches in complex real-world decision-making scenarios and risk evaluation.

Integrated trucks assignment and scheduling problem with mixed service mode docks: A Q-learning based adaptive large neighborhood search algorithm

Mixed service mode docks enhance efficiency by flexibly handling both loading and unloading trucks in warehouses. However, existing research often predetermines the number and location of these docks prior to planning truck assignment and sequencing. This paper proposes a new model integrating dock mode decision, truck assignment, and scheduling, thus enabling adaptive dock mode arrangements. Specifically, we introduce a Q-learning-based adaptive large neighborhood search (Q-ALNS) algorithm to address the integrated problem. The algorithm adjusts dock modes via perturbation operators, while truck assignment and scheduling are solved using destroy and repair local search operators. Q-learning adaptively selects these operators based on their performance history and future gains, employing the epsilon-greedy strategy. Extensive experimental results and statistical analysis indicate that the Q-ALNS benefits from efficient operator combinations and its adaptive mechanism, consistently outperforming benchmark algorithms in terms of optimality gap and Pareto front discovery. In comparison to the predetermined service mode, our adaptive strategy results in lower average tardiness and makespan, highlighting its superior adaptability to varying demands.

Dynamic operator management in meta-heuristics using reinforcement learning: an application to permutation flowshop scheduling problems

This study develops a framework based on reinforcement learning to dynamically manage a large portfolio of search operators within meta-heuristics. Using the idea of tabu search, the framework allows for continuous adaptation by temporarily excluding less efficient operators and updating the portfolio composition during the search. A Q-learning-based adaptive operator selection mechanism is used to select the most suitable operator from the dynamically updated portfolio at each stage. Unlike traditional approaches, the proposed framework requires no input from the experts regarding the search operators, allowing domain-specific non-experts to effectively use the framework. The performance of the proposed framework is analyzed through an application to the permutation flowshop scheduling problem. The results demonstrate the superior performance of the proposed framework against state-of-the-art algorithms in terms of optimality gap and convergence speed.