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Alan Malek

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14 papers

2 author rows

ICML Conference 2025 Conference Paper

FunBO: Discovering Acquisition Functions for Bayesian Optimization with FunSearch

Virginia Aglietti
Ira Ktena
Jessica Schrouff
Eleni Sgouritsa
Francisco J. R. Ruiz
Alan Malek
Alexis Bellot
Silvia Chiappa

The sample efficiency of Bayesian optimization algorithms depends on carefully crafted acquisition functions (AFs) guiding the sequential collection of function evaluations. The best-performing AFs can vary significantly across optimization problems, often requiring ad-hoc and problem-specific choices. This work tackles the challenge of designing novel AFs that perform well across a variety of experimental settings. Based on FunSearch, a recent work using Large Language Models (LLMs) for discovery in mathematical sciences, we propose FunBO, an LLM-based method that can be used to learn new AFs written in computer code by leveraging access to a number of evaluations for a limited set of objective functions. We provide the analytic expression of all discovered AFs and evaluate them on various global optimization benchmarks and hyperparameter optimization tasks. We show how FunBO identifies AFs that generalize well both in and out of the training distribution of functions, thus outperforming established general-purpose AFs and achieving competitive performance against AFs that are customized to specific function types and are learned via transfer-learning algorithms.

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NeurIPS Conference 2024 Conference Paper

Mind the Graph When Balancing Data for Fairness or Robustness

Jessica Schrouff
Alexis Bellot
Amal Rannen-Triki
Alan Malek
Isabela Albuquerque
Arthur Gretton
Alexander D'Amour
Silvia Chiappa

Failures of fairness or robustness in machine learning predictive settings can be due to undesired dependencies between covariates, outcomes and auxiliary factors of variation. A common strategy to mitigate these failures is data balancing, which attempts to remove those undesired dependencies. In this work, we define conditions on the training distribution for data balancing to lead to fair or robust models. Our results display that in many cases, the balanced distribution does not correspond to selectively removing the undesired dependencies in a causal graph of the task, leading to multiple failure modes and even interference with other mitigation techniques such as regularization. Overall, our results highlight the importance of taking the causal graph into account before performing data balancing.

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ICML Conference 2023 Conference Paper

Additive Causal Bandits with Unknown Graph

Alan Malek
Virginia Aglietti
Silvia Chiappa

We explore algorithms to select actions in the causal bandit setting where the learner can choose to intervene on a set of random variables related by a causal graph, and the learner sequentially chooses interventions and observes a sample from the interventional distribution. The learner’s goal is to quickly find the intervention, among all interventions on observable variables, that maximizes the expectation of an outcome variable. We depart from previous literature by assuming no knowledge of the causal graph except that latent confounders between the outcome and its ancestors are not present. We first show that the unknown graph problem can be exponentially hard in the parents of the outcome. To remedy this, we adopt an additional additive assumption on the outcome which allows us to solve the problem by casting it as an additive combinatorial linear bandit problem with full-bandit feedback. We propose a novel action-elimination algorithm for this setting, show how to apply this algorithm to the causal bandit problem, provide sample complexity bounds, and empirically validate our findings on a suite of randomly generated causal models, effectively showing that one does not need to explicitly learn the parents of the outcome to identify the best intervention.

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ICML Conference 2023 Conference Paper

Constrained Causal Bayesian Optimization

Virginia Aglietti
Alan Malek
Ira Ktena
Silvia Chiappa

We propose constrained causal Bayesian optimization (cCBO), an approach for finding interventions in a known causal graph that optimize a target variable under some constraints. cCBO first reduces the search space by exploiting the graph structure and, if available, an observational dataset; and then solves the restricted optimization problem by modelling target and constraint quantities using Gaussian processes and by sequentially selecting interventions via a constrained expected improvement acquisition function. We propose different surrogate models that enable to integrate observational and interventional data while capturing correlation among effects with increasing levels of sophistication. We evaluate cCBO on artificial and real-world causal graphs showing successful trade off between fast convergence and percentage of feasible interventions.

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NeurIPS Conference 2023 Conference Paper

Transportability for Bandits with Data from Different Environments

Alexis Bellot
Alan Malek
Silvia Chiappa

A unifying theme in the design of intelligent agents is to efficiently optimize a policy based on what prior knowledge of the problem is available and what actions can be taken to learn more about it. Bandits are a canonical instance of this task that has been intensely studied in the literature. Most methods, however, typically rely solely on an agent's experimentation in a single environment (or multiple closely related environments). In this paper, we relax this assumption and consider the design of bandit algorithms from a combination of batch data and qualitative assumptions about the relatedness across different environments, represented in the form of causal models. In particular, we show that it is possible to exploit invariances across environments, wherever they may occur in the underlying causal model, to consistently improve learning. The resulting bandit algorithm has a sub-linear regret bound with an explicit dependency on a term that captures how informative related environments are for the task at hand; and may have substantially lower regret than experimentation-only bandit instances.

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NeurIPS Conference 2022 Conference Paper

Anytime-Valid Inference For Multinomial Count Data

Michael Lindon
Alan Malek

Many experiments compare count outcomes among treatment groups. Examples include the number of successful signups in conversion rate experiments or the number of errors produced by software versions in canary tests. Observations typically arrive in a sequence and practitioners wish to continuously monitor their experiments, sequentially testing hypotheses while maintaining Type I error probabilities under optional stopping and continuation. These goals are frequently complicated in practice by non-stationary time dynamics. We provide practical solutions through sequential tests of multinomial hypotheses, hypotheses about many inhomogeneous Bernoulli processes and hypotheses about many time-inhomogeneous Poisson counting processes. For estimation, we further provide confidence sequences for multinomial probability vectors, all contrasts among probabilities of inhomogeneous Bernoulli processes and all contrasts among intensities of time-inhomogeneous Poisson counting processes. Together, these provide an ``anytime-valid'' inference framework for a wide variety of experiments dealing with count outcomes, which we illustrate with several industry applications.

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NeurIPS Conference 2021 Conference Paper

Asymptotically Best Causal Effect Identification with Multi-Armed Bandits

Alan Malek
Silvia Chiappa

This paper considers the problem of selecting a formula for identifying a causal quantity of interest among a set of available formulas. We assume an online setting in which the investigator may alter the data collection mechanism in a data-dependent way with the aim of identifying the formula with lowest asymptotic variance in as few samples as possible. We formalize this setting by using the best-arm-identification bandit framework where the standard goal of learning the arm with the lowest loss is replaced with the goal of learning the arm that will produce the best estimate. We introduce new tools for constructing finite-sample confidence bounds on estimates of the asymptotic variance that account for the estimation of potentially complex nuisance functions, and adapt the best-arm-identification algorithms of LUCB and Successive Elimination to use these bounds. We validate our method by providing upper bounds on the sample complexity and an empirical study on artificially generated data.

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JMLR Journal 2019 Journal Article

Best Arm Identification for Contaminated Bandits

Jason Altschuler
Victor-Emmanuel Brunel
Alan Malek

This paper studies active learning in the context of robust statistics. Specifically, we propose a variant of the Best Arm Identification problem for contaminated bandits, where each arm pull has probability epsilon of generating a sample from an arbitrary contamination distribution instead of the true underlying distribution. The goal is to identify the best (or approximately best) true distribution with high probability, with a secondary goal of providing guarantees on the quality of this distribution. The primary challenge of the contaminated bandit setting is that the true distributions are only partially identifiable, even with infinite samples. To address this, we develop tight, non-asymptotic sample complexity bounds for high-probability estimation of the first two robust moments (median and median absolute deviation) from contaminated samples. These concentration inequalities are the main technical contributions of the paper and may be of independent interest. Using these results, we adapt several classical Best Arm Identification algorithms to the contaminated bandit setting and derive sample complexity upper bounds for our problem. Finally, we provide matching information-theoretic lower bounds on the sample complexity (up to a small logarithmic factor). [abs] [ pdf ][ bib ] &copy JMLR 2019. ( edit, beta )

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NeurIPS Conference 2018 Conference Paper

Horizon-Independent Minimax Linear Regression

Alan Malek
Peter Bartlett

We consider online linear regression: at each round, an adversary reveals a covariate vector, the learner predicts a real value, the adversary reveals a label, and the learner suffers the squared prediction error. The aim is to minimize the difference between the cumulative loss and that of the linear predictor that is best in hindsight. Previous work demonstrated that the minimax optimal strategy is easy to compute recursively from the end of the game; this requires the entire sequence of covariate vectors in advance. We show that, once provided with a measure of the scale of the problem, we can invert the recursion and play the minimax strategy without knowing the future covariates. Further, we show that this forward recursion remains optimal even against adaptively chosen labels and covariates, provided that the adversary adheres to a set of constraints that prevent misrepresentation of the scale of the problem. This strategy is horizon-independent in that the regret and minimax strategies depend on the size of the constraint set and not on the time-horizon, and hence it incurs no more regret than the optimal strategy that knows in advance the number of rounds of the game. We also provide an interpretation of the minimax algorithm as a follow-the-regularized-leader strategy with a data-dependent regularizer and obtain an explicit expression for the minimax regret.

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NeurIPS Conference 2017 Conference Paper

Random Permutation Online Isotonic Regression

Wojciech Kotlowski
Wouter Koolen
Alan Malek

We revisit isotonic regression on linear orders, the problem of fitting monotonic functions to best explain the data, in an online setting. It was previously shown that online isotonic regression is unlearnable in a fully adversarial model, which lead to its study in the fixed design model. Here, we instead develop the more practical random permutation model. We show that the regret is bounded above by the excess leave-one-out loss for which we develop efficient algorithms and matching lower bounds. We also analyze the class of simple and popular forward algorithms and recommend where to look for algorithms for online isotonic regression on partial orders.

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ICML Conference 2015 Conference Paper

Large-Scale Markov Decision Problems with KL Control Cost and its Application to Crowdsourcing

Yasin Abbasi-Yadkori
Peter L. Bartlett
Xi Chen 0022
Alan Malek

We study average and total cost Markov decision problems with large state spaces. Since the computational and statistical costs of finding the optimal policy scale with the size of the state space, we focus on searching for near-optimality in a low-dimensional family of policies. In particular, we show that for problems with a Kullback-Leibler divergence cost function, we can reduce policy optimization to a convex optimization and solve it approximately using a stochastic subgradient algorithm. We show that the performance of the resulting policy is close to the best in the low-dimensional family. We demonstrate the efficacy of our approach by controlling the important crowdsourcing application of budget allocation in crowd labeling.

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NeurIPS Conference 2015 Conference Paper

Minimax Time Series Prediction

Wouter Koolen
Alan Malek
Peter Bartlett
Yasin Abbasi Yadkori

We consider an adversarial formulation of the problem ofpredicting a time series with square loss. The aim is to predictan arbitrary sequence of vectors almost as well as the bestsmooth comparator sequence in retrospect. Our approach allowsnatural measures of smoothness such as the squared norm ofincrements. More generally, we consider a linear time seriesmodel and penalize the comparator sequence through the energy ofthe implied driving noise terms. We derive the minimax strategyfor all problems of this type and show that it can be implementedefficiently. The optimal predictions are linear in the previousobservations. We obtain an explicit expression for the regret interms of the parameters defining the problem. For typical, simple definitions of smoothness, the computation of the optimalpredictions involves only sparse matrices. In the case ofnorm-constrained data, where the smoothness is defined in termsof the squared norm of the comparator's increments, we show thatthe regret grows as $T/\sqrt{\lambda_T}$, where $T$ is the lengthof the game and $\lambda_T$ is an increasing limit on comparatorsmoothness.

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NeurIPS Conference 2014 Conference Paper

Efficient Minimax Strategies for Square Loss Games

Wouter Koolen
Alan Malek
Peter Bartlett

We consider online prediction problems where the loss between the prediction and the outcome is measured by the squared Euclidean distance and its generalization, the squared Mahalanobis distance. We derive the minimax solutions for the case where the prediction and action spaces are the simplex (this setup is sometimes called the Brier game) and the $\ell_2$ ball (this setup is related to Gaussian density estimation). We show that in both cases the value of each sub-game is a quadratic function of a simple statistic of the state, with coefficients that can be efficiently computed using an explicit recurrence relation. The resulting deterministic minimax strategy and randomized maximin strategy are linear functions of the statistic.

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ICML Conference 2014 Conference Paper

Linear Programming for Large-Scale Markov Decision Problems

Alan Malek
Yasin Abbasi-Yadkori
Peter L. Bartlett

We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest goal of competing with a low-dimensional family of policies. We use the dual linear programming formulation of the MDP average cost problem, in which the variable is a stationary distribution over state-action pairs, and we consider a neighborhood of a low-dimensional subset of the set of stationary distributions (defined in terms of state-action features) as the comparison class. We propose two techniques, one based on stochastic convex optimization, and one based on constraint sampling. In both cases, we give bounds that show that the performance of our algorithms approaches the best achievable by any policy in the comparison class. Most importantly, these results depend on the size of the comparison class, but not on the size of the state space. Preliminary experiments show the effectiveness of the proposed algorithms in a queuing application.

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