Energy consumption has become a bottleneck for future computing architectures, from wearable devices to leadership-class supercomputers. Existing energy management techniques largely target CPUs, even though GPUs now dominate power draw in heterogeneous high performance computing (HPC) systems. Moreover, many prior methods rely on either purely offline or hybrid offline and online training, which is impractical and results in energy inefficiencies during data collection. In this paper, we introduce a practical online GPU energy optimization problem in a HPC scenarios. The problem is challenging because (1) GPU frequency scaling exhibits performance–energy trade-offs, (2) online control must balance exploration and exploitation, and (3) frequent frequency switching incurs non-trivial overhead and degrades quality of service (QoS). To address the challenges, we formulate online GPU energy optimization as a multi-armed bandit problem and propose EnergyUCB, a lightweight UCB-based controller that dynamically adjusts GPU core frequency in real time to save energy. Specifically, EnergyUCB (1) defines a reward that jointly captures energy and performance using a core-to-uncore utilization ratio as a proxy for GPU throughput, (2) employs optimistic initialization and UCB-style confidence bonuses to accelerate learning from scratch, and (3) incorporates a switching-aware UCB index and a QoS-constrained variant that enforce explicit slowdown budgets while discouraging unnecessary frequency oscillations. Extensive experiments on real-world workloads from the world's third fastest supercomputer Aurora show that EnergyUCB achieves substantial energy savings with modest slowdown and that the QoS-constrained variant reliably respects user-specified performance budgets.
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We study off-policy learning (OPL) in contextual bandits, which plays a key role in a wide range of real-world applications such as recommendation systems and online advertising. Typical OPL in contextual bandits assumes an unconstrained environment where a policy can select the same item infinitely. However, in many practical applications, including coupon allocation and e-commerce, limited supply constrains items through budget limits on distributed coupons or inventory restrictions on products. In these settings, greedily selecting the item with the highest expected reward for the current user may lead to early depletion of that item, making it unavailable for future users who could potentially generate higher expected rewards. As a result, OPL methods that are optimal in unconstrained settings may become suboptimal in limited supply settings. To address the issue, we provide a theoretical analysis showing that conventional greedy OPL approaches may fail to maximize the policy performance, and demonstrate that policies with superior performance must exist in limited supply settings. Based on this insight, we introduce a novel method called Off-Policy learning with Limited Supply (OPLS). Rather than simply selecting the item with the highest expected reward, OPLS focuses on items with relatively higher expected rewards compared to the other users, enabling more efficient allocation of items with limited supply. Our empirical results on both synthetic and real-world datasets show that OPLS outperforms existing OPL methods in contextual bandit problems with limited supply.
Motivated by the problem of assigning mediators to cases in the Kenyan judicial system, we study an online resource allocation problem where incoming tasks (cases) must be immediately assigned to available, capacity-constrained resources (mediators). The resources differ in their quality, which may need to be learned. In addition, resources can only be assigned to a subset of tasks that overlaps to varying degrees with the subset of tasks other resources can be assigned to. The objective is to maximize task completion while satisfying soft capacity constraints across all the resources. The scale of the real-world problem poses substantial challenges, since there are over 2000 mediators, and a multitude of combinations of geographic locations (87) and case types (12) that each mediator is qualified to work on. Together, these features—unknown quality of new resources (newly onboarded mediators), soft capacity constraints (due to the mandate to assign cases without delay), and high-dimensional state space—make existing scheduling and resource allocation algorithms either inapplicable or inefficient. We formalize the problem in a tractable manner, using a quadratic program formulation for assignment and a multi-agent bandit style framework for learning. We demonstrate the key properties and advantages of our new algorithm, SMaRT (Selecting Mediators that are Right for the Task), compared with baselines on some stylized instances of the mediator allocation problem. We then turn to considering its application to real-world data on cases and mediators from the Kenyan Judiciary. SMaRT outperforms baselines and allows for controlling the tradeoff between the strictness of the capacity constraints and overall case resolution rates, both in situations where mediator quality is known beforehand and when the problem is bandit-like in that learning is part of the problem definition. On the strength of these results, we plan to conduct a randomized controlled trial in which we deploy SMaRT in the Judiciary's mediation management system.
To make optimal joint pricing and inventory control decisions is a critical challenge for modern retailers. In practice, retailers face changing market conditions where demands are influenced by various contextual factors, while simultaneously dealing with the difficulty of lost sales that obscure true demand information. However, existing approaches often fail to account for both contextual information and censored demand observations. We address this gap by presenting a framework where we model demand as a linear combination of basis functions with unknown coefficients, allowing for adaptive pricing and inventory decisions that respond to changing contexts. We propose an efficient algorithm to achieve regret bound O(K sqrt(T) log T) under concave revenue conditions and O(K^(2/3) T^(2/3) (log T)^(1/2)) for the general case, with matching lower bounds confirming optimality. Extensive numerical experiments across diverse scenarios demonstrate our algorithm’s effectiveness.
In many multi-agent applications, tasks yield rewards only when executed by a coalition meeting an unknown size threshold; otherwise, feedback is fully censored. This censorship creates an identifiability problem: agents cannot distinguish stochastic failure from insufficient coordination. We formalize this setting as the Threshold-Activated Cooperative Multi-Armed Bandit (TAC-MAB) and analyze it under both centralized and decentralized coordination. We show that a centralized algorithm (C-TAC) achieves cumulative regret O(log T), decomposed into a structural-search term that captures the cost of resolving feasibility under censored feedback and a statistical-monitoring term for value estimation. We then introduce D-TAC, a decentralized event-triggered protocol in which agents synchronize only when their structural beliefs change. Empirically, D-TAC achieves a 23x reduction in communication relative to the centralized baseline while preserving feasibility alignment under conservative belief fusion. These results characterize the coordination cost of learning under censored feedback and show that near-centralized communication efficiency is achievable without continuous synchronization.
Offline-to-online reinforcement learning harnesses the stability of offline pretraining and the flexibility of online fine-tuning. A key challenge lies in the non-stationary distribution shift between offline datasets and the evolving online policy. Common approaches often rely on static mixing ratios or heuristic-based replay strategies, which lack adaptability to different environments and varying training dynamics, resulting in suboptimal tradeoff between stability and asymptotic performance. In this work, we propose Reinforcement Learning with Optimized Adaptive Data-mixing (ROAD), a dynamic plug-and-play framework that automates the data replay process. We identify a fundamental objective misalignment in existing approaches. To tackle this, we formulate the data selection problem as a bi-level optimization process, interpreting the data mixing strategy as a meta-decision governing the policy performance (outer-level) during online fine-tuning, while the conventional Q-learning updates operate at the inner level. To make it tractable, we propose a practical algorithm using a multi-armed bandit mechanism. This is guided by a surrogate objective which simultaneously maintains offline priors and prevents value overestimation. Our empirical results demonstrate that this approach consistently outperforms existing data replay methods across various datasets, eliminating the need for manual, context-specific adjustments while achieving superior stability and asymptotic performance.
This paper addresses the problem of learning to sparsify stochastic linear bandits, where a decision-maker sequentially selects actions from a high-dimensional space subject to a sparsity constraint on the number of nonzero elements in the action vector. The key challenge lies in minimizing cumulative regret while tackling the potential NP-hardness of finding optimal sparse actions due to the inherent combinatorial structure of the problem. We propose an adaptively phased exploration and exploitation algorithmic framework, utilizing ordinary least squares for parameter learning and specialized subroutines for sparse action selection. When the action set is a Euclidean ball, optimal sparse actions can be efficiently computed, enabling us to establish a Õ(d √T) regret, where d is the dimension of the action vector and T is the time horizon length. For general convex and compact action sets where finding optimal sparse actions is intractable, we employ a greedy subroutine. For general strongly convex action sets, we derive a Õ(d √T) α-regret; for general compact sets lacking strong convexity, we establish a Õ(d T^(2/3)) α-regret, where α pertains to the approximation ratio of the greedy algorithm. Finally, we validate the performance of our algorithms using extensive experiments.
Efficient Contextual Bandit Learning via Reward-Space Sampling and Online Optimization (Student Abstract)
PDF ↗The contextual multi-armed bandit problem underlies applications in recommendations, e-commerce, finance, and healthcare, where balancing exploration and exploitation is critical. While algorithms such as Upper Confidence Bound (UCB) and Thompson Sampling (TS) achieve strong theoretical guarantees, they often incur heavy computational cost from high-dimensional parameter estimation. We propose a new approach that combines reward sampling with online stochastic optimization. At each round, the algorithm samples hypothetical rewards for all actions and selects the action with the largest draw; the observed reward then updates the model via stochastic optimization. This design is both simple and efficient, preserving exploration while avoiding the pitfalls of greedy behavior on near-duplicate arms. Across synthetic and real-world datasets, our method attains near-optimal reward more quickly and with substantially lower computation than TS and UCB, demonstrating that sampling directly in reward space can improve both statistical efficiency and scalability.
A Multi-Agent Conversational Bandit Approach to Online Evaluation and Selection of User-Aligned LLM Responses
PDF ↗Prompt-based offline methods are commonly used to optimize large language model (LLM) responses, but evaluating these responses is computationally intensive and often fails to accommodate diverse response styles. This study introduces a novel online evaluation framework that employs a multi-agent conversational bandit model to select optimal responses while aligning with user preferences dynamically. To tackle challenges such as high-dimensional features, large response sets, adaptive conversational needs, and multi-device access, we propose MACO, Multi-Agent Conversational Online Learning, which comprises two key components: (1) MACO-A: Executed by local agents, it employs an online elimination mechanism to filter out low-quality responses. (2) MACO-S: Executed by the cloud server, it adaptively adjusts selection strategies based on aggregated preference data. An adaptive preference mechanism triggers asynchronous conversations to enhance alignment efficiency. Theoretical analysis demonstrates that MACO achieves near-optimal regret bounds, matching state-of-the-art performance in various degenerate cases. Extensive experiments utilizing Google and OpenAI text embedding models on the real-world datasets with different response styles, combined with Llama and GPT-4o, show that MACO consistently outperforms baseline methods by at least 8.29% across varying response set sizes and numbers of agents.
Offline policy learning from logged data is a critical paradigm for enabling effective decision-making without costly online exploration. However, its application has been largely confined to single-objective problems, a stark contrast to real-world scenarios where decision-making inherently involves navigating multiple, often conflicting, objectives. This paper introduces a comprehensive framework for Offline Multi-Objective Bandits (OffMOB), providing a principled solution to the fundamental challenge of learning Pareto-optimal policies from a static dataset. Our core contribution is a novel algorithm that uniquely integrates the pessimism principle with multi-objective optimization to safely learn from off-policy data. Crucially, our approach transcends the primary limitation of scalarization techniques, which are restricted to finding a single policy for a pre-defined preference. Instead, OffMOB directly approximates the entire Pareto front, learning a single, flexible policy model capable of generating an optimal action for any desired trade-off. To rigorously evaluate performance, we introduce the Tchebycheff sub-optimality metric and establish the first finite-sample generalization bounds for this problem class, proving that our algorithm converges to the true Pareto front under practical data coverage assumptions. Extensive experiments on complex benchmarks demonstrate that OffMOB significantly outperforms existing methods, identifying the complete set of optimal trade-offs where naive extensions fail.
Large language models (LLMs) exhibit diverse response behaviors, costs, and strengths, making it challenging to select the most suitable LLM for a given user query. We study the problem of adaptive multi-LLM selection in an online setting, where the learner interacts with users through multi-step query refinement and must choose LLMs sequentially without access to offline datasets or model internals. A key challenge arises from unstructured context evolution: the prompt dynamically changes in response to previous model outputs via a black-box process, which cannot be simulated, modeled, or learned. To address this, we propose the first contextual bandit framework for sequential LLM selection under unstructured prompt dynamics. We formalize a notion of myopic regret and develop a LinUCB-based algorithm that provably achieves sublinear regret without relying on future context prediction. We further introduce budget-aware and positionally-aware (favoring early-stage satisfaction) extensions to accommodate variable query costs and user preferences for early high-quality responses. Our algorithms are theoretically grounded and require no offline fine-tuning or dataset-specific training. Experiments on diverse benchmarks demonstrate that our methods outperform existing LLM routing strategies in both accuracy and cost-efficiency, validating the power of contextual bandits for real-time, adaptive LLM selection.
We present a novel framework for online learning in Stackelberg general-sum games, where two agents, the leader and follower, engage in sequential turn-based interactions. At the core of this approach is a learned diffeomorphism that maps the joint action space to a smooth spherical Riemannian manifold, referred to as the Stackelberg manifold. This mapping, facilitated by neural normalizing flows, ensures the formation of tractable isoplanar subspaces, enabling efficient techniques for online learning. Leveraging the linearity of the agents' reward functions on the Stackelberg manifold, our construct allows the application of linear bandit algorithms. We then provide a rigorous theoretical basis for regret minimization on the learned manifold and establish bounds on the simple regret for learning Stackelberg equilibrium. This integration of manifold learning into game theory uncovers a previously unrecognized potential for neural normalizing flows as an effective tool for multi-agent learning. We present empirical results demonstrating the effectiveness of our approach compared to standard baselines, with applications spanning domains such as cybersecurity and economic supply chain optimization.
Contextual linear dueling bandits have recently garnered significant attention due to their widespread applications in important domains such as recommender systems and large language models. Classical dueling bandit algorithms are typically only applicable to a single agent. However, many applications of dueling bandits involve multiple agents who wish to collaborate for improved performance yet are unwilling to share their data. This motivates us to draw inspirations from federated learning, which involves multiple agents aiming to collaboratively train their neural networks via gradient descent (GD) without sharing their raw data. Previous works have developed federated linear bandit algorithms which rely on closed-form updates of the bandit parameters (e.g., the linear function parameters) to achieve collaboration. However, in linear dueling bandits, the linear function parameters lack a closed-form expression and their estimation requires minimizing a loss function. This renders these previous methods inapplicable. In this work, we overcome this challenge through an innovative and principled combination of online gradient descent (OGD, for minimizing the loss function to estimate the linear function parameters) and federated learning, hence introducing our federated linear dueling bandit with OGD (FLDB-OGD) algorithm. Through rigorous theoretical analysis, we prove that FLDB-OGD enjoys a sub-linear upper bound on its cumulative regret and demonstrate a theoretical trade-off between regret and communication complexity. We conduct empirical experiments to demonstrate the effectiveness of FLDB-OGD and reveal valuable insights, such as the benefit of a larger number of agents, the regret-communication trade-off, among others.
Automated red-teaming has emerged as a scalable approach for auditing Large Language Models (LLMs) prior to deployment, yet existing approaches lack mechanisms to efficiently adapt to model-specific vulnerabilities at inference. We introduce Red-Bandit, a red-teaming framework that adapts online to identify and exploit model failure modes under distinct attack styles (e.g., manipulation, slang). Red-Bandit post-trains a set of parameter-efficient LoRA experts, each specialized for a particular attack style, using reinforcement learning that rewards the generation of unsafe prompts via a rule-based safety model. At inference, a multi-armed bandit policy dynamically selects among these attack-style experts based on the target model’s response safety, balancing exploration and exploitation. Red-Bandit outperforms state-of-the-art methods on AdvBench and HarmBench, achieving higher attack success rates under sufficient exploration budgets (ASR@10), while generating more human-readable adversarial prompts (lower perplexity). In addition, Red-Bandit’s bandit policy serves as a diagnostic tool for identifying model-specific vulnerabilities by indicating which attack styles most effectively elicit harmful behaviors.
General Machine Learning · Online Learning, Active Learning and Bandits
We study a widely used Bayesian optimization method, Gaussian process Thompson sampling (GP-TS), under the assumption that the objective function is a sample path from a GP. Compared with the GP upper confidence bound (GP-UCB) with established high-probability and expected regret bounds, most analyses of GP-TS have been limited to expected regret. Moreover, whether the recent analyses of GP-UCB for the lenient regret and the improved cumulative regret upper bound can be applied to GP-TS remains unclear. To fill these gaps, this paper shows several regret bounds: (i) a regret lower bound for GP-TS, which implies that GP-TS suffers from a polynomial dependence on $1/\delta$ with probability $\delta$, (ii) an upper bound of the second moment of cumulative regret, which directly suggests an improved regret upper bound on $\delta$, (iii) expected lenient regret upper bounds, and (iv) an improved cumulative regret upper bound on the time horizon $T$. Along the way, we provide several useful lemmas, including a relaxation of the necessary condition from recent analysis to obtain improved regret upper bounds on $T$.
Theory · Online Learning and Bandits
We study the revenue of approximate correlated equilibrium in discrete first price auctions - the set of allowable bids is $\mathcal{B} = \{0, 1/k, \dots, 1 - 1/k, 1\}$ for some $k \in \mathbb{N}$. We show that the revenue of any $\epsilon$-\textit{approximate} correlated equilibrium is at least $v_2 - \Theta(1/k)- \Theta(\epsilon k^2)$, where $v_2 \geq 0$ is the second-highest valuation. Our results establish the first polynomial convergence rates on the revenue generated by no-swap regret bidders in first-price auctions. For instance, if bidders admit the optimal swap regret of $\mathcal{O}(\sqrt{k T})$, then the time-averaged revenue is at least $v_2 - \Theta(1/k) - \Theta(\epsilon)$ after $\mathcal{O}(k^5/\epsilon^2)$ rounds.
Theory · Online Learning and Bandits
We consider the question of how to employ next-token prediction algorithms in adversarial online decision making environments. Specifically, if we train a next-token prediction model on a distribution $\mathcal{D}$ over sequences of opponent actions, when is it the case that the induced online decision making algorithm (by approximately best responding to the model's predictions) has low adversarial regret (i.e., when is $\mathcal{D}$ a \emph{low-regret distribution})? For unbounded context windows (where the prediction made by the model can depend on all the actions taken by the adversary thus far), we show that although not every distribution $\mathcal{D}$ is a low-regret distribution, every distribution $\mathcal{D}$ is exponentially close (in TV distance) to one low-regret distribution, and hence sublinear regret can always be achieved at negligible cost to the accuracy of the original next-token prediction model. In contrast to this, for bounded context windows (where the prediction made by the model can depend only on the past $w$ actions taken by the adversary, as may be the case in modern transformer architectures), we show that there are some distributions $\mathcal{D}$ of opponent play that are $\Theta(1)$-far from any low-regret distribution $\mathcal{D'}$ (even when $w = \Omega(T)$ and such distributions exist). Finally, we complement these results by showing that the unbounded context robustification procedure can be implemented by layers of a standard transformer architecture, and provide empirical evidence that transformer models can be efficiently trained to represent these new low-regret distributions.
General Machine Learning · Online Learning, Active Learning and Bandits
Bagging-based ensembles, most notably Adaptive Random Forests, are among the strongest performers for learning from data streams. A common denominator across these methods is their reliance on Hoeffding Trees as base learners, which grow incrementally by testing whether a candidate split is significantly better than its alternatives using concentration inequalities. Despite their empirical success, existing Hoeffding Trees variants lack valid statistical guarantees. Current analyses rely on fixed-sample concentration bounds, while split decisions are made using data-dependent stopping rules, which invalidates their guarantees and can drive the probabilty of incorrect splits to one. We introduce a principled alternative based on \emph{anytime-valid inference}. Our method provides: (i) anytime-valid control of false splits under arbitrary data streams, including non-stationary settings; (ii) finite commitment time under a predictive advantage; and (iii) under stationary i.i.d.\ data, risk is monotone decreasing and strictly improves at every split. Empirically, we evaluate both standalone trees and their use within Adaptive Random Forests on non-stationary streams. Our method improves performance while producing substantially smaller trees.
General Machine Learning · Online Learning, Active Learning and Bandits
We revisit the standard perturbation-based approach of Abernethy et al. (2008) in the context of unconstrained Bandit Linear Optimization (uBLO). We show the surprising result that in the unconstrained setting, this approach effectively reduces Bandit Linear Optimization (BLO) to a standard Online Linear Optimization (OLO) problem. Our framework improves on prior work in several ways. First, we derive expected-regret guarantees when our perturbation scheme is combined with comparator-adaptive OLO algorithms, leading to new insights about the impact of different adversarial models on the resulting comparator-adaptive rates. We extend our analysis to dynamic regret, obtaining the optimal $\sqrt{P_T}$ path-length dependencies without prior knowledge of $P_T$. We then develop the first high-probability guarantees for both static and dynamic regret in uBLO. Finally, we discuss lower bounds on the static regret, and prove the folklore $\Omega(\sqrt{dT})$ rate for adversarial linear bandits on the unit Euclidean ball, which is of independent interest.
Efficient Online Influence Maximization under the Independent Cascade Model with Node-Level Feedback
Theory · Online Learning and Bandits
Influence maximization is an important research area in social network analysis, where the goal is to select a small set of seed nodes so as to maximize the expected spread of influence under a stochastic diffusion process. Classical approximation algorithms for this problem rely on full knowledge of the underlying influence probabilities and operate in an offline manner. In many real-world settings, however, these probabilities are unknown and must be learned from data, raising the question: \emph{can one still obtain strong performance guarantees while simultaneously learning the diffusion model parameters through repeated interactions?} In this paper, we study the problem of \emph{online influence maximization} under the independent cascade model, where influence probabilities are unknown and feedback is limited to \emph{node-level} activation outcomes. Prior work relies on a \emph{pair oracle} which needs to perform a joint optimization over seed sets and feasible parameters. This oracle is difficult to implement in practice and it was open whether one can achieve sublinear regret using only a \emph{standard} offline oracle. We resolve this question by designing an online learning algorithm that achieves $\widetilde{O}(\sqrt{T})$ regret using only a \emph{standard} offline oracle. Finally, we validate our theoretical results via experiments on real and synthetic data.