We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small cumulative constraints violation across the $T$ rounds. We present the first best-of-both-world type algorithm for this general class of problems, with no-regret guarantees both in the case in which rewards and constraints are selected according to an unknown stochastic model, and in the case in which they are selected at each round by an adversary. Our algorithm is the first to provide guarantees in the adversarial setting with respect to the optimal fixed strategy that satisfies the long-term constraints. In particular, it guarantees a $\rho/(1+\rho)$ fraction of the optimal reward and sublinear regret, where $\rho$ is a feasibility parameter related to the existence of strictly feasible solutions. Our framework employs traditional regret minimizers as black-box components. Therefore, by instantiating it with an appropriate choice of regret minimizers it can handle the full-feedback as well as the bandit-feedback setting. Moreover, it allows the decision maker to seamlessly handle scenarios with non-convex rewards and constraints. We show how our framework can be applied in the context of budget-management mechanisms for repeated auctions in order to guarantee long-term constraints that are not packing (e.g., ROI constraints).
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The interplay between Machine Learning (ML) and Constrained Optimization (CO) has recently been the subject of increasing interest, leading to a new and prolific research area covering (e.g.) Decision Focused Learning and Constrained Reinforcement Learning. Such approaches strive to tackle complex decision problems under uncertainty over multiple stages, involving both explicit (cost function, constraints) and implicit knowledge (from data), and possibly subject to execution time restrictions. While a good degree of success has been achieved, the existing methods still have limitations in terms of both applicability and effectiveness. For problems in this class, we propose UNIFY, a unified framework to design a solution policy for complex decision-making problems. Our approach relies on a clever decomposition of the policy in two stages, namely an unconstrained ML model and a CO problem, to take advantage of the strength of each approach while compensating for its weaknesses. With a little design effort, UNIFY can generalize several existing approaches, thus extending their applicability. We demonstrate the method effectiveness on two practical problems, namely an Energy Management System and the Set Multi-cover with stochastic coverage requirements. Finally, we highlight some current challenges of our method and future research directions that can benefit from the cross-fertilization of the two fields.
Real-world optimization problems may have a different underlying structure. In black-box optimization, the dependencies between decision variables remain unknown. However, some techniques can discover such interactions accurately. In Large Scale Global Optimization (LSGO), problems are high-dimensional. It was shown effective to decompose LSGO problems into subproblems and optimize them separately. The effectiveness of such approaches may be highly dependent on the accuracy of problem decomposition. Many state-of-the-art decomposition strategies are derived from Differential Grouping (DG). However, if a given problem consists of non-additively separable subproblems, DG-based strategies may discover many non-existing interactions. On the other hand, monotonicity checking strategies proposed so far do not report non-existing interactions for any separable subproblems but may miss discovering many of the existing ones. Therefore, we propose Incremental Recursive Ranking Grouping (IRRG) that suffers from none of these flaws. IRRG consumes more fitness function evaluations than the recent DG-based propositions, e.g., Recursive DG 3 (RDG3). Nevertheless, the effectiveness of the considered Cooperative Co-evolution frameworks after embedding IRRG or RDG3 was similar for problems with additively separable subproblems that are suitable for RDG3. After replacing the additive separability with non-additive, embedding IRRG leads to results of significantly higher quality.
The study of leakage measures for privacy has been a subject of intensive research and is an important aspect of understanding how privacy leaks occur in computer programs. Differential privacy has been a focal point in the privacy community for some years and yet its leakage characteristics are not completely understood. In this paper we bring together two areas of research -- information theory and the g-leakage framework of quantitative information flow (QIF) -- to give an operational interpretation for the epsilon parameter of differential privacy. We find that epsilon emerges as a capacity measure in both frameworks; via (log)-lift, a popular measure in information theory; and via max-case g-leakage, which describes the leakage of any system to Bayesian adversaries modelled using ``worst-case'' assumptions under the QIF framework. Our characterisation resolves an important question of interpretability of epsilon and consolidates a number of disparate results covering the literature of both information theory and quantitative information flow.
In distributed or federated optimization and learning, communication between the different computing units is often the bottleneck and gradient compression is widely used to reduce the number of bits sent within each communication round of iterative methods. There are two classes of compression operators and separate algorithms making use of them. In the case of unbiased random compressors with bounded variance (e.g., rand-k), the DIANA algorithm of Mishchenko et al. (2019), which implements a variance reduction technique for handling the variance introduced by compression, is the current state of the art. In the case of biased and contractive compressors (e.g., top-k), the EF21 algorithm of Richt\'arik et al. (2021), which instead implements an error-feedback mechanism, is the current state of the art. These two classes of compression schemes and algorithms are distinct, with different analyses and proof techniques. In this paper, we unify them into a single framework and propose a new algorithm, recovering DIANA and EF21 as particular cases. Our general approach works with a new, larger class of compressors, which has two parameters, the bias and the variance, and includes unbiased and biased compressors as particular cases. This allows us to inherit the best of the two worlds: like EF21 and unlike DIANA, biased compressors, like top-k, whose good performance in practice is recognized, can be used. And like DIANA and unlike EF21, independent randomness at the compressors allows to mitigate the effects of compression, with the convergence rate improving when the number of parallel workers is large. This is the first time that an algorithm with all these features is proposed. We prove its linear convergence under certain conditions. Our approach takes a step towards better understanding of two so-far distinct worlds of communication-efficient distributed learning.
Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems. Our framework follows a standard relaxation-plus-rounding approach and adopts neural networks to parameterize the relaxed solutions so that simple back-propagation can train the model end-to-end. Our key contribution is the observation that if the relaxed objective satisfies entry-wise concavity, a low optimization loss guarantees the quality of the final integral solutions. This observation significantly broadens the applicability of the previous framework inspired by Erdos' probabilistic method. In particular, this observation can guide the design of objective models in applications where the objectives are not given explicitly while requiring being modeled in prior. We evaluate our framework by solving a synthetic graph optimization problem, and two real-world applications including resource allocation in circuit design and approximate computing. Our framework largely outperforms the baselines based on na\"{i}ve relaxation, reinforcement learning, and Gumbel-softmax tricks.
Long-term fairness is an important factor of consideration in designing and deploying learning-based decision systems in high-stake decision-making contexts. Recent work has proposed the use of Markov Decision Processes (MDPs) to formulate decision-making with long-term fairness requirements in dynamically changing environments, and demonstrated major challenges in directly deploying heuristic and rule-based policies that worked well in static environments. We show that policy optimization methods from deep reinforcement learning can be used to find strictly better decision policies that can often achieve both higher overall utility and less violation of the fairness requirements, compared to previously-known strategies. In particular, we propose new methods for imposing fairness requirements in policy optimization by regularizing the advantage evaluation of different actions. Our proposed methods make it easy to impose fairness constraints without reward engineering or sacrificing training efficiency. We perform detailed analyses in three established case studies, including attention allocation in incident monitoring, bank loan approval, and vaccine distribution in population networks.
In domains where sample sizes are limited, efficient learning algorithms are critical. Learning using privileged information (LuPI) offers increased sample efficiency by allowing prediction models access to auxiliary information at training time which is unavailable when the models are used. In recent work, it was shown that for prediction in linear-Gaussian dynamical systems, a LuPI learner with access to intermediate time series data is never worse and often better in expectation than any unbiased classical learner. We provide new insights into this analysis and generalize it to nonlinear prediction tasks in latent dynamical systems, extending theoretical guarantees to the case where the map connecting latent variables and observations is known up to a linear transform. In addition, we propose algorithms based on random features and representation learning for the case when this map is unknown. A suite of empirical results confirm theoretical findings and show the potential of using privileged time-series information in nonlinear prediction.
The problem of monotone submodular maximization has been studied extensively due to its wide range of applications. However, there are cases where one can only access the objective function in a distorted or noisy form because of the uncertain nature or the errors involved in the evaluation. This paper considers the problem of constrained monotone submodular maximization with noisy oracles introduced by [Hassidim et al., 2017]. For a cardinality constraint, we propose an algorithm achieving a near-optimal $\left(1-\frac{1}{e}-O(\varepsilon)\right)$-approximation guarantee (for arbitrary $\varepsilon > 0$) with only a polynomial number of queries to the noisy value oracle, which improves the exponential query complexity of [Singer et al., 2018]. For general matroid constraints, we show the first constant approximation algorithm in the presence of noise. Our main approaches are to design a novel local search framework that can handle the effect of noise and to construct certain smoothing surrogate functions for noise reduction.
Bayesian optimization (BO) is a popular approach for sample-efficient optimization of black-box objective functions. While BO has been successfully applied to a wide range of scientific applications, traditional approaches to single-objective BO only seek to find a single best solution. This can be a significant limitation in situations where solutions may later turn out to be intractable. For example, a designed molecule may turn out to violate constraints that can only be reasonably evaluated after the optimization process has concluded. To address this issue, we propose Rank-Ordered Bayesian Optimization with Trust-regions (ROBOT) which aims to find a portfolio of high-performing solutions that are diverse according to a user-specified diversity metric. We evaluate ROBOT on several real-world applications and show that it can discover large sets of high-performing diverse solutions while requiring few additional function evaluations compared to finding a single best solution.
Action anticipation involves predicting future actions having observed the initial portion of a video. Typically, the observed video is processed as a whole to obtain a video-level representation of the ongoing activity in the video, which is then used for future prediction. We introduce ANTICIPATR which performs long-term action anticipation leveraging segment-level representations learned using individual segments from different activities, in addition to a video-level representation. We propose a two-stage learning approach to train a novel transformer-based model that uses these two types of representations to directly predict a set of future action instances over any given anticipation duration. Results on Breakfast, 50Salads, Epic-Kitchens-55, and EGTEA Gaze+ datasets demonstrate the effectiveness of our approach.
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