Heesang Ann, Hyunjun Choi, Taehyun Hwang +3stat.ML cs.LG
We study generalized linear bandits with memory, an endogenous non-stationary setting in which rewards depend on past actions through a finite memory matrix. Building on prior work for linear models (Clerici et al., 2024), we show that the previously known $\tilde{O}(T^{3/4})$ regret bound stems from a loose analysis, and we provide a sharpened analysis that recovers a $\tilde{O}(\sqrt{T})$ regret rate in the linear case. We then extend this improvement to generalized linear models and propose a block-wise algorithm based on shrunken confidence bounds. Our algorithm achieves a regret bound of $\tilde{O}\left(\sqrt{mT} + d\sqrt{T} + \sqrtκ\, d^{2} m^{1/4} T^{1/4} + κd^{2} \right)$, where $d$ denotes the feature dimension, $m$ the memory length, and $κ$ a curvature parameter of the link function. This attains a $\sqrt{T}$-type rate despite nonlinear rewards and memory effects. To the best of our knowledge, this analysis provides a unified treatment of memory-induced non-stationarity and nonlinear link functions, while ensuring that the leading regret term is independent of the curvature of the link function. We conduct numerical experiments that are consistent with our theoretical findings.
We study the contextual dynamic pricing problem under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model that can change over time. The demand model is assumed to be a generalized linear model (GLM), allowing for a feature vector in $\mathbb{R}^d$ that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential changes. We propose a multiscale change-point detection based algorithm that achieves a regret of order $\widetilde{O}(\sqrt{s_TdT}\wedge\{V_T^{1/3}d^{1/3}T^{2/3}+\sqrt{dT}\})$, where $s_T$ is the number of piecewise stationary segments and $V_T$ is a newly defined notion of design-adjusted variation budget of model parameters. Our algorithm is adaptive and does not require knowing $s_T$ or $V_T$. Moreover, to our knowledge, this is the first dynamic pricing algorithm that is adaptive to the nature of changes and achieves the best-of-both-worlds rate, thus closing a long-standing gap in the literature. We remark that, due to the varying contexts, existing works in the adaptive non-stationary bandit literature cannot be applied to achieve optimality for contextual dynamic pricing. The regret is further accompanied with a newly constructed minimax lower bound, confirming the optimality of our algorithm (up to logarithmic factors). Extensive numerical experiments are conducted to illustrate the efficiency and robustness of the proposed algorithm in non-stationary dynamic pricing.
This paper introduces Periodic Bootstrap Thompson Sampling (PBTS), an innovative extension of the classic Thompson Sampling (TS) algorithm tailored for bandit problems with periodic non-stationarity. Conventional TS accumulates all past observations, leading to biased posteriors when reward distributions cycle over time. PBTS overcomes this by synchronizing belief resets with known or inferred period intervals and embedding structured bootstrap exploration phases, effectively purging obsolete data while preserving uncertainty estimates. PBTS is tested in artificially constructed environments, which include skewed and balanced reward distributions, along with different bootstrap proportions and misaligned periodic intervals. Results indicate that PBTS generally achieves statistically significant reductions in cumulative regret against traditional TS in periodic non-stationary environments. Subsequent discussion further articulates the potential of PBTS's real-world deployment. The study mentions limitations like extreme periodic misalignment and proposes future research such as self-adjusting cycle-recognition. With memory reset and bootstrap phase, PBTS introduces a novel approach to optimizing bandit algorithms in periodic reward contexts.
L. A. Zhukov, E. V. Shaburova, D. V. Antonetscs.LG
Bayesian optimization is increasingly used to guide data-efficient experimentation in chemistry, materials science, and related laboratory settings, but its practical performance depends strongly on how well surrogate-model assumptions match the geometry and noise structure of the underlying objective. We introduce tidyHEBO, a robust Bayesian optimization model inspired by heteroskedastic evolutionary Bayesian optimization (HEBO) for single-objective, sequential optimization. tidyHEBO reconstructs the HEBO design philosophy in BoTorch and revises surrogate training, output-warping selection, acquisition function evaluation, and Pareto-front search. We benchmarked tidyHEBO on synthetic functions, Olympus emulators, fully experimental reaction-optimization datasets, needle-in-a-haystack (NIAH) materials problems, and Bayesmark hyperparameter optimization tasks. On these tasks tidyHEBO achieved competitive to superior performance and improvement in robustness across repeated optimization runs. We therefore propose tidyHEBO as a practical tool for sequential experimentations and a strong general-purpose benchmark for future Bayesian optimization research.
We study non-stationary linear contextual bandits where the reward model drifts over time, rendering classical contextual bandit algorithms brittle because historical data becomes systematically biased. We propose Flow-Corrected Thompson Sampling (fcTS), a Bayesian method that reuses experience by transporting past rewards to the present using an explicit drift model and incorporating each transported observation with a confidence weight that reflects transport reliability. This yields a unified template that specializes in (i) linear parameter drift via online slope estimation and reward correction, (ii) periodic variation via phase-aware reuse across cycles, and (iii) recurring regime switches via changepoint detection and regime-specific posterior memory. The resulting posterior updates remain closed-form under a linear Gaussian model and can be implemented efficiently with truncated, incrementally updated sufficient statistics. Across five controlled case studies and a semi-synthetic portfolio-selection benchmark with multiple overlapping non-stationarities, fcTS outperforms standard forgetting-based baselines (discounting, sliding windows, and periodic restarts), with the largest gains in settings exhibiting recurring temporal structure. These results demonstrate that when non-stationarity is structured, correcting and reweighting historical observations can be substantially more sample-efficient than uniformly discarding them.
We consider a variant of the linear contextual stochastic multi-armed bandits, where the learner must provide recommendations to a group of users, each having its personalized preference vector, and in the presence of context distributions that are drifting over time. Under practitioner-friendly assumptions, we reduce this setting to linear bandit with stationary mean but heteroskedastic and non-stationary noise. We further study the case when the learner must ensure the mean reward of each decision must exceed that of a baseline strategy $\boldsymbolπ_0$ at each decision step. We introduce Dri-MED, an algorithm inspired from the linear version of the MED strategy, and carefully adapted to handle the non-stationary heteroskedastic noise. We show that the instance-dependent regret scales as $\tilde{\mathcal O}\left(\fracκ{\tildeΔ}d^2(\log(T)\right)$, where $\tildeΔ$ is the constraint-aware sub-optimality gap subject to policy $π_0$, with variance-aware multiplicative term $κ$ that we carefully handle using heteroskedastic regression. We further show Dri-MED enjoys $\tilde{\mathcal{O}}(d)$ expected constraint violations. Our numerical results suggest that Dri-MED significantly outperforms conservative baselines that ignores the drift and preference structure.
This paper investigates non-stationary online learning using the metric of interval regret, which requires an online algorithm to perform well over every time interval. We propose the first online learning algorithm that achieves an interval regret bound scaling with gradient variation, a fundamental measure of the cumulative change in online function gradients, which relates to various problem-dependent quantities and is closely connected to stochastic optimization and other problems. Our method employs a simple and efficient two-layer online ensemble structure that achieves strong theoretical guarantees. Specifically, it enjoys a regret bound that simultaneously adapts to various problem-dependent quantities while also preserving the minimax-optimal rate in the worst case. Moreover, recognizing the challenge of hyperparameter tuning, we introduce a Lipschitz- and smoothness-agnostic variant that automatically adapts to these potentially unknown constants. This is primarily enabled by a novel Lipschitz-adaptive meta algorithm, which may be of independent interest. Beyond interval regret, our method also yields broader implications: it provides versatile bounds for interval dynamic regret, a stronger measure that competes with changing comparators over any interval, and yields the first piecewise characterization for stochastic extended adversarial optimization. Theoretical findings are validated by experiments.