arXiv:2607. 06879v1 Announce Type: new Abstract: Best-arm identification is a canonical model for data-driven decision-making, but in many applications each reward observation is costly.
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The paper introduces a new variant of the multi‑armed bandit problem that incorporates dueling feedback—pairwise comparisons of model responses—and heterogeneous sampling costs to identify the best large language model (LLM) from a set with varying query costs. Assuming a Condorcet winner, the authors propose a Track‑and‑Stop style algorithm that guarantees asymptotically optimal cost as the error probability approaches zero. Extensive experiments on synthetic and real‑world data show that this cost‑aware approach consistently outperforms both classical cost‑unaware algorithms and other cost‑aware extensions.
The paper introduces SELECT, an algorithmic framework for satisficing regret minimization in bandit problems, achieving constant expected satisficing regret when a satisficing arm exists. A variant, SELECT‑LITE, further ensures a light‑tailed satisficing regret distribution while maintaining constant expected regret in the realizable case and sub‑linear standard regret otherwise. Experiments on synthetic data and a real‑world dynamic pricing scenario demonstrate the practical effectiveness of both algorithms.
The paper presents a new scaling law for reward optimization in AI alignment, showing that performance scales as Θ(√min{log(M), K}), where M is the number of preference comparisons used to train a proxy reward model and K is the KL‑divergence budget relative to a reference policy. The authors derive this law using an information‑theoretic model, prove its tightness, and validate it with extensive experiments involving a 70B gold reward model and smaller proxy models (0.6B–4B). The empirical results demonstrate a strong fit (R² 97–99 %) across different model sizes, noise levels, and optimization methods, suggesting that reward optimization behaves like a simple selection task over IID Gaussian variables with noisy feedback.
arXiv:2607. 14706v1 Announce Type: new Abstract: We design and analyze \underline{M}echanism-\underline{E}nforced \underline{S}equential \underline{HA}lving (MESHA), an algorithm for Best Arm Identification (BAI) in strategic linear bandits.
arXiv:2605. 09448v2 Announce Type: replace Abstract: We study the operational problem of automated bidding in repeated first-price auctions under budget and return-on-spend (RoS) constraints.
arXiv:2608. 06545v1 Announce Type: new Abstract: Distributionally robust Markov decision processes provide a principled framework for sequential decision making under model uncertainty.