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Stephen Pasteris

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14

TMLR Journal 2025 Journal Article

A Hierarchical Nearest Neighbour Approach to Contextual Bandits

  • Stephen Pasteris
  • Madeleine Dwyer
  • Chris Hicks
  • Vasilios Mavroudis

In this paper we consider the contextual bandit problem in metric spaces. We design and analyse an algorithm that can handle the fully adversarial problem in which no assumptions are made about the space itself, or the generation of contexts and losses. In addition to analysing our performance on general metric spaces, we further analyse the important special case in which the space is euclidean, and furthermore analyse the i.i.d. stochastic setting. Unlike previous work our algorithm is adaptive to the local density of contexts and the smoothness of the decision boundary of the comparator policy, as well as other quantities. Our algorithm is highly efficient - having a per-trial time polylogarithmic in both the number of trials and the number of actions when the dimensionality of the metric space is bounded. We also give the results of real world experiments, demonstrating the excellent performance of our algorithm.

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NeurIPS Conference 2025 Conference Paper

Statistical Parity with Exponential Weights

  • Stephen Pasteris
  • Chris Hicks
  • Vasilios Mavroudis

Statistical parity is one of the most foundational constraints in algorithmic fairness and privacy. In this paper, we show that statistical parity can be enforced efficiently in the adversarial contextual bandit setting while retaining strong performance guarantees. Specifically, we present a meta-algorithm that transforms any efficient implementation of Hedge (or, equivalently, any discrete Bayesian inference algorithm) into an efficient contextual bandit algorithm that guarantees exact statistical parity on every trial. Compared to any comparator that satisfies the same statistical parity constraint, the algorithm achieves the same asymptotic regret bound as running the equivalent instance of Exp4 for each group. We also address the scenario where the target parity distribution is unknown and must be estimated online. Finally, using online-to-batch conversion, we extend our approach to the batch classification setting.

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NeurIPS Conference 2024 Conference Paper

Bandits with Abstention under Expert Advice

  • Stephen Pasteris
  • Alberto Rumi
  • Maximilian Thiessen
  • Shota Saito
  • Atsushi Miyauchi
  • Fabio Vitale
  • Mark Herbster

We study the classic problem of prediction with expert advice under bandit feedback. Our model assumes that one action, corresponding to the learner's abstention from play, has no reward or loss on every trial. We propose the CBA (Confidence-rated Bandits with Abstentions) algorithm, which exploits this assumption to obtain reward bounds that can significantly improve those of the classical Exp4 algorithm. Our problem can be construed as the aggregation of confidence-rated predictors, with the learner having the option to abstain from play. We are the first to achieve bounds on the expected cumulative reward for general confidence-rated predictors. In the special case of specialists, we achieve a novel reward bound, significantly improving previous bounds of SpecialistExp (treating abstention as another action). We discuss how CBA can be applied to the problem of adversarial contextual bandits with the option of abstaining from selecting any action. We are able to leverage a wide range of inductive biases, outperforming previous approaches both theoretically and in preliminary experimental analysis. Additionally, we achieve a reduction in runtime from quadratic to almost linear in the number of contexts for the specific case of metric space contexts.

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NeurIPS Conference 2024 Conference Paper

Online Convex Optimisation: The Optimal Switching Regret for all Segmentations Simultaneously

  • Stephen Pasteris
  • Chris Hicks
  • Vasilios Mavroudis
  • Mark Herbster

We consider the classic problem of online convex optimisation. Whereas the notion of static regret is relevant for stationary problems, the notion of switching regret is more appropriate for non-stationary problems. A switching regret is defined relative to any segmentation of the trial sequence, and is equal to the sum of the static regrets of each segment. In this paper we show that, perhaps surprisingly, we can achieve the asymptotically optimal switching regret on every possible segmentation simultaneously. Our algorithm for doing so is very efficient: having a space and per-trial time complexity that is logarithmic in the time-horizon. Our algorithm also obtains novel bounds on its dynamic regret: being adaptive to variations in the rate of change of the comparator sequence.

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EWRL Workshop 2024 Workshop Paper

Sum-Max Submodular Bandits

  • Stephen Pasteris
  • Alberto Rumi
  • Fabio Vitale
  • Nicolò Cesa-Bianchi

Many online decision-making problems correspond to maximizing a sequence of submodular functions. In this work, we introduce sum-max functions, a subclass of monotone submodular functions capturing several interesting problems, including best-of-$K$-bandits, combinatorial bandits, and the bandit versions on $M$-medians and hitting sets. We show that all functions in this class satisfy a key property that we call pseudo-concavity. This allows us to prove $\big(1 - \frac{1}{e}\big)$-regret bounds for bandit feedback in the nonstochastic setting of the order of $\sqrt{MKT}$ (ignoring log factors), where $T$ is the time horizon and $M$ is a cardinality constraint. This bound, attained by a simple and efficient algorithm, significantly improves on the $\widetilde{\mathcal{O}}\big(T^{2/3}\big)$ regret bound for online monotone submodular maximization with bandit feedback. We also extend our results to a bandit version of the facility location problem.

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NeurIPS Conference 2023 Conference Paper

Nearest Neighbour with Bandit Feedback

  • Stephen Pasteris
  • Chris Hicks
  • Vasilios Mavroudis

In this paper we adapt the nearest neighbour rule to the contextual bandit problem. Our algorithm handles the fully adversarial setting in which no assumptions at all are made about the data-generation process. When combined with a sufficiently fast data-structure for (perhaps approximate) adaptive nearest neighbour search, such as a navigating net, our algorithm is extremely efficient - having a per trial running time polylogarithmic in both the number of trials and actions, and taking only quasi-linear space. We give generic regret bounds for our algorithm and further analyse them when applied to the stochastic bandit problem in euclidean space. A side result of this paper is that, when applied to the online classification problem with stochastic labels, our algorithm can, under certain conditions, have sublinear regret whilst only finding a single nearest neighbour per trial - in stark contrast to the k-nearest neighbours algorithm.

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NeurIPS Conference 2021 Conference Paper

A Gang of Adversarial Bandits

  • Mark Herbster
  • Stephen Pasteris
  • Fabio Vitale
  • Massimiliano Pontil

We consider running multiple instances of multi-armed bandit (MAB) problems in parallel. A main motivation for this study are online recommendation systems, in which each of $N$ users is associated with a MAB problem and the goal is to exploit users' similarity in order to learn users' preferences to $K$ items more efficiently. We consider the adversarial MAB setting, whereby an adversary is free to choose which user and which loss to present to the learner during the learning process. Users are in a social network and the learner is aided by a-priori knowledge of the strengths of the social links between all pairs of users. It is assumed that if the social link between two users is strong then they tend to share the same action. The regret is measured relative to an arbitrary function which maps users to actions. The smoothness of the function is captured by a resistance-based dispersion measure $\Psi$. We present two learning algorithms, GABA-I and GABA-II, which exploit the network structure to bias towards functions of low $\Psi$ values. We show that GABA-I has an expected regret bound of $\mathcal{O}(\sqrt{\ln(NK/\Psi)\Psi KT})$ and per-trial time complexity of $\mathcal{O}(K\ln(N))$, whilst GABA-II has a weaker $\mathcal{O}(\sqrt{\ln(N/\Psi)\ln(NK/\Psi)\Psi KT})$ regret, but a better $\mathcal{O}(\ln(K)\ln(N))$ per-trial time complexity. We highlight improvements of both algorithms over running independent standard MABs across users.

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NeurIPS Conference 2021 Conference Paper

Cooperative Stochastic Bandits with Asynchronous Agents and Constrained Feedback

  • Lin Yang
  • Yu-Zhen Janice Chen
  • Stephen Pasteris
  • Mohammad Hajiesmaili
  • John C. S. Lui
  • Don Towsley

This paper studies a cooperative multi-armed bandit problem with $M$ agents cooperating together to solve the same instance of a $K$-armed stochastic bandit problem with the goal of maximizing the cumulative reward of agents. The agents are heterogeneous in (i) their limited access to a local subset of arms; and (ii) their decision-making rounds, i. e. , agents are asynchronous with different decision-making gaps. The goal is to find the global optimal arm and agents are able to pull any arm, however, they observe the reward only when the selected arm is local. The challenge is a tradeoff for agents between pulling a local arm with the possibility of observing the feedback, or relying on the observations of other agents that might occur at different rates. Naive extensions of traditional algorithms lead to an arbitrarily poor regret as a function of aggregate action frequency of any $\textit{suboptimal}$ arm located in slow agents. We resolve this issue by proposing a novel two-stage learning algorithm, called $\texttt{CO-LCB}$ algorithm, whose regret is a function of aggregate action frequency of agents containing the $\textit{optimal}$ arm. We also show that the regret of $\texttt{CO-LCB}$ matches the regret lower bound up to a small factor.

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NeurIPS Conference 2020 Conference Paper

Online Matrix Completion with Side Information

  • Mark Herbster
  • Stephen Pasteris
  • Lisa Tse

We give an online algorithm and prove novel mistake and regret bounds for online binary matrix completion with side information. The mistake bounds we prove are of the form \tilde{O}(D/\gamma^2). The term 1/\gamma^2 is analogous to the usual margin term in SVM (perceptron) bounds. More specifically, if we assume that there is some factorization of the underlying m x n matrix into PQ^T, where the rows of P are interpreted as "classifiers" in R^d and the rows of Q as "instances" in R^d, then gamma is the maximum (normalized) margin over all factorizations PQ^T consistent with the observed matrix. The quasi-dimension term D measures the quality of side information. In the presence of vacuous side information, D = m+n. However, if the side information is predictive of the underlying factorization of the matrix, then in an ideal case, D \in O(k + l) where k is the number of distinct row factors and l is the number of distinct column factors. We additionally provide a generalization of our algorithm to the inductive setting. In this setting, we provide an example where the side information is not directly specified in advance. For this example, the quasi-dimension D is now bounded by O(k^2 + l^2).

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NeurIPS Conference 2020 Conference Paper

Online Multitask Learning with Long-Term Memory

  • Mark Herbster
  • Stephen Pasteris
  • Lisa Tse

We introduce a novel online multitask setting. In this setting each task is partitioned into a sequence of segments that is unknown to the learner. Associated with each segment is a hypothesis from some hypothesis class. We give algorithms that are designed to exploit the scenario where there are many such segments but significantly fewer associated hypotheses. We prove regret bounds that hold for any segmentation of the tasks and any association of hypotheses to the segments. In the single-task setting this is equivalent to switching with long-term memory in the sense of [Bousquet and Warmuth 2011]. We provide an algorithm that predicts on each trial in time linear in the number of hypotheses when the hypothesis class is finite. We also consider infinite hypothesis classes from reproducing kernel Hilbert spaces for which we give an algorithm whose per trial time complexity is cubic in the number of cumulative trials. In the single-task special case this is the first example of an efficient regret-bounded switching algorithm with long-term memory for a non-parametric hypothesis class.

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NeurIPS Conference 2016 Conference Paper

Mistake Bounds for Binary Matrix Completion

  • Mark Herbster
  • Stephen Pasteris
  • Massimiliano Pontil

We study the problem of completing a binary matrix in an online learning setting. On each trial we predict a matrix entry and then receive the true entry. We propose a Matrix Exponentiated Gradient algorithm [1] to solve this problem. We provide a mistake bound for the algorithm, which scales with the margin complexity [2, 3] of the underlying matrix. The bound suggests an interpretation where each row of the matrix is a prediction task over a finite set of objects, the columns. Using this we show that the algorithm makes a number of mistakes which is comparable up to a logarithmic factor to the number of mistakes made by the Kernel Perceptron with an optimal kernel in hindsight. We discuss applications of the algorithm to predicting as well as the best biclustering and to the problem of predicting the labeling of a graph without knowing the graph in advance.

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NeurIPS Conference 2015 Conference Paper

Online Prediction at the Limit of Zero Temperature

  • Mark Herbster
  • Stephen Pasteris
  • Shaona Ghosh

We design an online algorithm to classify the vertices of a graph. Underpinning the algorithm is the probability distribution of an Ising model isomorphic to the graph. Each classification is based on predicting the label with maximum marginal probability in the limit of zero-temperature with respect to the labels and vertices seen so far. Computing these classifications is unfortunately based on a $\#P$-complete problem. This motivates us to develop an algorithm for which we give a sequential guarantee in the online mistake bound framework. Our algorithm is optimal when the graph is a tree matching the prior results in [1]. For a general graph, the algorithm exploits the additional connectivity over a tree to provide a per-cluster bound. The algorithm is efficient as the cumulative time to sequentially predict all of the vertices of the graph is quadratic in the size of the graph.

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JMLR Journal 2015 Journal Article

Predicting a Switching Sequence of Graph Labelings

  • Mark Herbster
  • Stephen Pasteris
  • Massimiliano Pontil

We study the problem of predicting online the labeling of a graph. We consider a novel setting for this problem in which, in addition to observing vertices and labels on the graph, we also observe a sequence of just vertices on a second graph. A latent labeling of the second graph selects one of $K$ labelings to be active on the first graph. We propose a polynomial time algorithm for online prediction in this setting and derive a mistake bound for the algorithm. The bound is controlled by the geometric cut of the observed and latent labelings, as well as the resistance diameters of the graphs. When specialized to multitask prediction and online switching problems the bound gives new and sharper results under certain conditions. [abs] [ pdf ][ bib ] &copy JMLR 2015. ( edit, beta )

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