arXiv Machine Learning

Online Resource Allocation with an Endogenous Markov State: Fewer LP Solves Earn More

arXiv Machine Learning
6d ago

Online Generalized-Mean Welfare Maximization: Achieving Near-Optimal Regret from Samples

The paper investigates online fair allocation of sequential items to agents with heterogeneous preferences, aiming to maximize generalized-mean welfare. In an i.i.d. arrival setting, a pure greedy algorithm achieves near-optimal “~O(1/T)” average regret without needing distributional knowledge. For nonstationary arrivals, the authors show that a single historical sample per distribution suffices to recover the same regret rate, using re-solving algorithms that remain robust to distribution shifts.

By Zongjun Yang, Rachitesh Kumar, Christian Kroer
arXiv Machine Learning
Oct 2

Learning Infinite-Horizon Average-Reward CMDPs via State Augmentation

The paper introduces a computationally efficient algorithm for infinite-horizon average-reward constrained Markov decision processes (CMDPs) under weak communication. It achieves a high-probability regret and cumulative constraint violation of ×O(√T) in the tabular setting, matching optimal dependence up to logarithmic factors. The method augments the state with cumulative constraint violation, reshapes rewards using a Huber potential, and applies finite-horizon approximation with optimistic value iteration to maintain bounded per-step rewards.

By Kihyun Yu, Seoungbin Bae, Dabeen Lee