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Optimal Dynamic Regret by Transformers for Non-Stationary Reinforcement Learning
Transformers have demonstrated exceptional performance across a wide range of domains. While their ability to perform reinforcement learning in-context has been established both theoretically and empirically, their behavior in nonstationary environments remains less understood. In this study, we address this gap by showing that transformers can achieve nearly optimal dynamic regret bounds in non-stationary settings. We prove that transformers are capable of approximating strategies used to handle non-stationary environments and can learn the approximator in the in-context learning setup. Our experiments further show that transformers can match or even outperform existing expert algorithms in such environments.
Towards Accelerated Model Training via Bayesian Data Selection
Mislabeled, duplicated, or biased data in real-world scenarios can lead to prolonged training and even hinder model convergence. Traditional solutions prioritizing easy or hard samples lack the flexibility to handle such a variety simultaneously. Recent work has proposed a more reasonable data selection principle by examining the data's impact on the model's generalization loss. However, its practical adoption relies on less principled approximations and additional holdout data. This work solves these problems by leveraging a lightweight Bayesian treatment and incorporating off-the-shelf zero-shot predictors built on large-scale pre-trained models. The resulting algorithm is efficient and easy to implement. We perform extensive empirical studies on challenging benchmarks with considerable data noise and imbalance in the online batch selection scenario, and observe superior training efficiency over competitive baselines. Notably, on the challenging WebVision benchmark, our method can achieve similar predictive performance with significantly fewer training iterations than leading data selection methods.
Optimizing Conditional Value-At-Risk of Black-Box Functions
This paper presents two Bayesian optimization (BO) algorithms with theoretical performance guarantee to maximize the conditional value-at-risk (CVaR) of a black-box function: CV-UCB and CV-TS which are based on the well-established principle of optimism in the face of uncertainty and Thompson sampling, respectively. To achieve this, we develop an upper confidence bound of CVaR and prove the no-regret guarantee of CV-UCB by utilizing an interesting connection between CVaR and value-at-risk (VaR). For CV-TS, though it is straightforwardly performed with Thompson sampling, bounding its Bayesian regret is non-trivial because it requires a tail expectation bound for the distribution of CVaR of a black-box function, which has not been shown in the literature. The performances of both CV-UCB and CV-TS are empirically evaluated in optimizing CVaR of synthetic benchmark functions and simulated real-world optimization problems.
Learning Survival Models with Right-Censored Reporting Delays
Shikuri, Yuta, Fujisawa, Hironori
Survival analysis is a statistical technique used to estimate the time until an event occurs. Although it is applied across a wide range of fields, adjusting for reporting delays under practical constraints remains a significant challenge in the insurance industry. Such delays render event occurrences unobservable when their reports are subject to right censoring. This issue becomes particularly critical when estimating hazard rates for newly enrolled cohorts with limited follow-up due to administrative censoring. Our study addresses this challenge by jointly modeling the parametric hazard functions of event occurrences and report timings. The joint probability distribution is marginalized over the latent event occurrence status. We construct an estimator for the proposed survival model and establish its asymptotic consistency. Furthermore, we develop an expectation-maximization algorithm to compute its estimates. Using these findings, we propose a two-stage estimation procedure based on a parametric proportional hazards model to evaluate observations subject to administrative censoring. Experimental results demonstrate that our method effectively improves the timeliness of risk evaluation for newly enrolled cohorts.
Online Convex Optimization with Heavy Tails: Old Algorithms, New Regrets, and Applications
In Online Convex Optimization (OCO), when the stochastic gradient has a finite variance, many algorithms provably work and guarantee a sublinear regret. However, limited results are known if the gradient estimate has a heavy tail, i.e., the stochastic gradient only admits a finite $\mathsf{p}$-th central moment for some $\mathsf{p}\in\left(1,2\right]$. Motivated by it, this work examines different old algorithms for OCO (e.g., Online Gradient Descent) in the more challenging heavy-tailed setting. Under the standard bounded domain assumption, we establish new regrets for these classical methods without any algorithmic modification. Remarkably, these regret bounds are fully optimal in all parameters (can be achieved even without knowing $\mathsf{p}$), suggesting that OCO with heavy tails can be solved effectively without any extra operation (e.g., gradient clipping). Our new results have several applications. A particularly interesting one is the first provable convergence result for nonsmooth nonconvex optimization under heavy-tailed noise without gradient clipping. Furthermore, we explore broader settings (e.g., smooth OCO) and extend our ideas to optimistic algorithms to handle different cases simultaneously.