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新论文 · v1arXiv:2611.04275

Online Metric Matching with Unknown i.i.d. Arrivals

Tsubasa Harada

原文摘要

We study online metric matching with $n$ servers and $n$ requests drawn independently from an unknown distribution. Each request must be matched immediately and irrevocably to an unused server, and the algorithm receives no samples before the process starts. We give a randomized algorithm that is $O((\log\log\log n)^2)$-competitive on arbitrary metric spaces and $O(1)$-competitive on tree metrics. These guarantees match the corresponding bounds for known i.i.d. request distributions in [GGPW19] up to constant factors. More generally, our competitive ratio is $O(α(n))$ whenever the Fair-Bias algorithm introduced in that work has competitive ratio $α(n)$ for known i.i.d. arrivals on the same class of metrics. Consequently, proving that Fair-Bias is constant-competitive on general metrics would also yield a constant-competitive algorithm for unknown i.i.d. arrivals.

cs.DS

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.02739

Beyond Monotonicity: Stochastic Online Optimization under Semi-Bandit Feedback

Tsubasa Harada, Yasushi Kawase, Hanna Sumita

原文摘要

We study stochastic online optimization (SOO) under semi-bandit feedback: in each of $T$ rounds, a policy adaptively observes $n$ independent random variables with unknown distributions, learning only from observed values. First-order stochastic dominance (FSD) monotonicity enables general reductions for learning SOO, but can fail when observations change future feasibility, resource use, or reference points. Our algorithm runs the dynamic program for the optimal policy, replacing each expectation by its most optimistic value over a confidence set of distributions. Its regret depends on the level-set complexity $s_i$ of the computed values as functions of the $i$th variable: the number of intervals needed to describe their superlevel sets. For rewards in $[0,1]$, the regret is $\tilde{O}(\sqrt{ST})$ without this monotonicity, where $S=\sum_{i=1}^n\min\{s_i,k_i\}$ and $k_i$ is the support size of the $i$th distribution, which may be infinite when $s_i$ is finite. For constant level-set complexities, regret is $\tilde{O}(\sqrt{nT})$, even for continuous distributions. The algorithm requires no knowledge of $s_i$, $k_i$, or the supports, and it also achieves regret $\tilde{O}(\sqrt{nkT})$ for supports of size at most $k$ without any level-set condition, which improves the previous bound $\tilde{O}(n(\sqrt{kT}+k))$ for FSD-monotone problems. We also prove a lower bound of $Ω(\min\{T,\sqrt{ST}\})$ for all positive integers $s_1,\ldots,s_n$ with $k_i=2s_i+1$, which holds even under full feedback and matches the upper bound up to logarithmic factors. We obtain $\tilde{O}(\sqrt{nT})$ regret for these problems, all nonmonotone under FSD: stochastic Boolean function evaluation, the full-information secretary problem, optimal stopping with loss aversion, scheduling with deadlines and correlated stochastic knapsack with unimodal rewards, and overbooking with group reservations.

cs.LG

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