Adaptive Selective Sampling for Online Prediction with Experts
Eindhoven University of Technology（埃因霍温理工大学）；Eindhoven Artificial Intelligence Systems Institute (EAISI)（埃因霍温人工智能系统研究所（EAISI））；University College London（伦敦大学学院）；University of Amsterdam（阿姆斯特丹大学）
We consider online prediction of a binary sequence with expert advice. For this setting, we devise label-efficient forecasting algorithms, which use a selective sampling scheme that enables collecting much fewer labels than standard procedures, while still retaining optimal worst-case regret guarantees. These algorithms are based on exponentially weighted forecasters, suitable for settings with and without a perfect expert. For a scenario where one expert is strictly better than the others in expectation, we show that the label complexity of the label-efficient forecaster scales roughly as the square root of the number of rounds. Finally, we present numerical experiments empirically showing that the normalized regret of the label-efficient forecaster can asymptotically match known minimax rates for pool-based active learning, suggesting it can optimally adapt to benign settings.
Online imitation learning is the problem of how best to mimic expert demonstrations, given access to the environment or an accurate simulator. Prior work has shown that in the infinite sample regime, exact moment matching achieves value equivalence to the expert policy. However, in the finite sample regime, even if one has no optimization error, empirical variance can lead to a performance gap that scales with $H^2 / N$ for behavioral cloning and $H / \sqrt{N}$ for online moment matching, where $H$ is the horizon and $N$ is the size of the expert dataset. We introduce the technique of replay e…
Efficient conformal prediction intervals for time series: Online PID-Expert aggregation
School of Economics and Management, Beihang University（北京航空航天大学经济管理学院）；Beijing Shuji Intelligent Technology Co., Ltd.（北京数智科技有限公司）；Center for Forecasting Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院预测科学中心）
Heinz College（海因茨学院）；Department of Statistics（统计系）
We explore the problem of learning under selective labels in the context of algorithm-assisted decision making. Selective labels is a pervasive selection bias problem that arises when historical decision making blinds us to the true outcome for certain instances. Examples of this are common in many applications, ranging from predicting recidivism using pre-trial release data to diagnosing patients. In this paper we discuss why selective labels often cannot be effectively tackled by standard methods for adjusting for sample selection bias, even if there are no unobservables. We propose a data a…
Motivated by applications to resource-limited and safety-critical domains, we study selective classification in the online learning model, wherein a predictor may abstain from classifying an instance. For example, this may model an adaptive decision to invoke more resources on this instance. Two salient aspects of the setting we consider are that the data may be non-realisable, due to which abstention may be a valid long-term action, and that feedback is only received when the learner abstains, which models the fact that reliable labels are only available when the resource intensive processing…
In this work, we aim to create a completely online algorithmic framework for prediction with expert advice that is translation-free and scale-free of the expert losses. Our goal is to create a generalized algorithm that is suitable for use in a wide variety of applications. For this purpose, we study the expected regret of our algorithm against a generic competition class in the sequential prediction by expert advice problem, where the expected regret measures the difference between the losses of our prediction algorithm and the losses of the 'best' expert selection strategy in the competition…
Online learning with expert advice is widely used in various machine learning tasks. It considers the problem where a learner chooses one from a set of experts to take advice and make a decision. In many learning problems, experts may be related, henceforth the learner can observe the losses associated with a subset of experts that are related to the chosen one. In this context, the relationship among experts can be captured by a feedback graph, which can be used to assist the learner's decision making. However, in practice, the nominal feedback graph often entails uncertainties, which renders…
Institute for Information Transmission Problems, Moscow（莫斯科信息传输问题研究所）
We develop the setting of sequential prediction based on shifting experts and on a "smooth" version of the method of specialized experts. To aggregate experts predictions, we use the AdaHedge algorithm, which is a version of the Hedge algorithm with adaptive learning rate, and extend it by the meta-algorithm Fixed Share. Due to this, we combine the advantages of both algorithms: (1) we use the shifting regret which is a more optimal characteristic of the algorithm; (2) regret bounds are valid in the case of signed unbounded losses of the experts. Also, (3) we incorporate in this scheme a "smoo…
School of Computing, National University of Singapore（新加坡国立大学计算机学院）；Fédération ENAC ISAE-SUPAERO ONERA, Université de Toulouse, France（法国图卢兹大学ENAC ISAE-SUPAERO ONERA联合体）；Institute for Infocomm Research, A*STAR , Singapore（新加坡A*STAR信息通信研究所）；IPAL, IRL 2955, Singapore（新加坡IPAL实验室）；Department of Mathematics, National University of Singapore（新加坡国立大学数学系）
In many real life situations, including job and loan applications, gatekeepers must make justified and fair real-time decisions about a person's fitness for a particular opportunity. In this paper, we aim to accomplish approximate group fairness in an online stochastic decision-making process, where the fairness metric we consider is equalized odds. Our work follows from the classical learning-from-experts scheme, assuming a finite set of classifiers (human experts, rules, options, etc) that cannot be modified. We run separate instances of the algorithm for each label class as well as sensitiv…
DeepMind（深度思考）；OpenAI；University of California, Berkeley（加州大学伯克利分校）；Google Brain（谷歌大脑）
Monte Carlo Tree Search (MCTS) algorithms perform simulation-based search to improve policies online. During search, the simulation policy is adapted to explore the most promising lines of play. MCTS has been used by state-of-the-art programs for many problems, however a disadvantage to MCTS is that it estimates the values of states with Monte Carlo averages, stored in a search tree; this does not scale to games with very high branching factors. We propose an alternative simulation-based search method, Policy Gradient Search (PGS), which adapts a neural network simulation policy online via pol…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）
For the prediction with experts' advice setting, we construct forecasting algorithms that suffer loss not much more than any expert in the pool. In contrast to the standard approach, we investigate the case of long-term forecasting of time series and consider two scenarios. In the first one, at each step $t$ the learner has to combine the point forecasts of the experts issued for the time interval $[t+1, t+d]$ ahead. Our approach implies that at each time step experts issue point forecasts for arbitrary many steps ahead and then the learner (algorithm) combines these forecasts and the forecast…
In this article, we aim at improving the prediction of expert aggregation by using the underlying properties of the models that provide expert predictions. We restrict ourselves to the case where expert predictions come from Kalman recursions, fitting state-space models. By using exponential weights, we construct different algorithms of Kalman recursions Aggregated Online (KAO) that compete with the best expert or the best convex combination of experts in a more or less adaptive way. We improve the existing results on expert aggregation literature when the experts are Kalman recursions by taki…
This paper considers a variant of the classical online learning problem with expert predictions. Our model's differences and challenges are due to lacking any direct feedback on the loss each expert incurs at each time step $t$. We propose an approach that uses peer prediction and identify conditions where it succeeds. Our techniques revolve around a carefully designed peer score function $s()$ that scores experts' predictions based on the peer consensus. We show a sufficient condition, that we call \emph{peer calibration}, under which standard online learning algorithms using loss feedback co…
We study the multiclass online learning problem where a forecaster makes a sequence of predictions using the advice of $n$ experts. Our main contribution is to analyze the regime where the best expert makes at most $b$ mistakes and to show that when $b = o(\log_4{n})$, the expected number of mistakes made by the optimal forecaster is at most $\log_4{n} + o(\log_4{n})$. We also describe an adversary strategy showing that this bound is tight and that the worst case is attained for binary prediction.
Toyota Technological Institute at Chicago（芝加哥丰田工学院）
We study the problem of online learning with primary and secondary losses. For example, a recruiter making decisions of which job applicants to hire might weigh false positives and false negatives equally (the primary loss) but the applicants might weigh false negatives much higher (the secondary loss). We consider the following question: Can we combine "expert advice" to achieve low regret with respect to the primary loss, while at the same time performing {\em not much worse than the worst expert} with respect to the secondary loss? Unfortunately, we show that this goal is unachievable witho…
Università degli Studi di Milano（米兰大学）；ETH Zürich（苏黎世联邦理工学院）
We consider prediction with expert advice for strongly convex and bounded losses, and investigate trade-offs between regret and "variance" (i.e., squared difference of learner's predictions and best expert predictions). With $K$ experts, the Exponentially Weighted Average (EWA) algorithm is known to achieve $O(\log K)$ regret. We prove that a variant of EWA either achieves a negative regret (i.e., the algorithm outperforms the best expert), or guarantees a $O(\log K)$ bound on both variance and regret. Building on this result, we show several examples of how variance of predictions can be expl…
Online (Non-)Convex Learning via Tempered Optimism
Inria（法国国家信息与自动化技术研究所）；Ecole Normale Supérieure（法国高等科学研究院）；PSL Research University（巴黎综合理工学院）；Sorbonne Université（索邦大学）；University College London（伦敦大学学院）
A key challenge in online learning is that classical algorithms can be slow to adapt to changing environments. Recent studies have proposed "meta" algorithms that convert any online learning algorithm to one that is adaptive to changing environments, where the adaptivity is analyzed in a quantity called the strongly-adaptive regret. This paper describes a new meta algorithm that has a strongly-adaptive regret bound that is a factor of $\sqrt{\log(T)}$ better than other algorithms with the same time complexity, where $T$ is the time horizon. We also extend our algorithm to achieve a first-order…
National Key Laboratory for Novel Software Technology（Novel Software Technology国家重点实验室）；Nanjing University（南京大学）
In this paper, we consider the problem of prediction with expert advice in dynamic environments. We choose tracking regret as the performance metric and develop two adaptive and efficient algorithms with data-dependent tracking regret bounds. The first algorithm achieves a second-order tracking regret bound, which improves existing first-order bounds. The second algorithm enjoys a path-length bound, which is generally not comparable to the second-order bound but offers advantages in slowly moving environments. Both algorithms are developed under the online mirror descent framework and draw ins…
We consider prediction with expert advice under the log-loss with the goal of deriving efficient and robust algorithms. We argue that existing algorithms such as exponentiated gradient, online gradient descent and online Newton step do not adequately satisfy both requirements. Our main contribution is an analysis of the Prod algorithm that is robust to any data sequence and runs in linear time relative to the number of experts in each round. Despite the unbounded nature of the log-loss, we derive a bound that is independent of the largest loss and of the largest gradient, and depends only on t…
Technion – Israel Institute of Technology（以色列理工学院）；Deepmind；Nvidia Research（英伟达研究院）
In Apprenticeship Learning (AL), we are given a Markov Decision Process (MDP) without access to the cost function. Instead, we observe trajectories sampled by an expert that acts according to some policy. The goal is to find a policy that matches the expert's performance on some predefined set of cost functions. We introduce an online variant of AL (Online Apprenticeship Learning; OAL), where the agent is expected to perform comparably to the expert while interacting with the environment. We show that the OAL problem can be effectively solved by combining two mirror descent based no-regret alg…
We consider online learning problems where the aim is to achieve regret which is efficient in the sense that it is the same order as the lowest regret amongst K experts. This is a substantially stronger requirement that achieving $O(\sqrt{n})$ or $O(\log n)$ regret with respect to the best expert and standard algorithms are insufficient, even in easy cases where the regrets of the available actions are very different from one another. We show that a particular lazy form of the online subgradient algorithm can be used to achieve minimal regret in a number of "easy" regimes while retaining an $O…
We consider the decision-making framework of online convex optimization with a very large number of experts. This setting is ubiquitous in contextual and reinforcement learning problems, where the size of the policy class renders enumeration and search within the policy class infeasible. Instead, we consider generalizing the methodology of online boosting. We define a weak learning algorithm as a mechanism that guarantees multiplicatively approximate regret against a base class of experts. In this access model, we give an efficient boosting algorithm that guarantees near-optimal regret against…
Georgia Tech（佐治亚理工学院）；University of Washington（华盛顿大学）；Microsoft Research（微软研究院）
Online imitation learning (IL) is an algorithmic framework that leverages interactions with expert policies for efficient policy optimization. Here policies are optimized by performing online learning on a sequence of loss functions that encourage the learner to mimic expert actions, and if the online learning has no regret, the agent can provably learn an expert-like policy. Online IL has demonstrated empirical successes in many applications and interestingly, its policy improvement speed observed in practice is usually much faster than existing theory suggests. In this work, we provide an ex…
We consider a basic problem at the interface of two fundamental fields: submodular optimization and online learning. In the online unconstrained submodular maximization (online USM) problem, there is a universe $[n]=\{1,2,...,n\}$ and a sequence of $T$ nonnegative (not necessarily monotone) submodular functions arrive over time. The goal is to design a computationally efficient online algorithm, which chooses a subset of $[n]$ at each time step as a function only of the past, such that the accumulated value of the chosen subsets is as close as possible to the maximum total value of a fixed sub…
Microsoft Research NYC（微软研究院纽约分部）；DIMACS Center, Rutgers University（罗格斯大学DIMACS中心）；Harvard University（哈佛大学）
We study online learning settings in which experts act strategically to maximize their influence on the learning algorithm's predictions by potentially misreporting their beliefs about a sequence of binary events. Our goal is twofold. First, we want the learning algorithm to be no-regret with respect to the best fixed expert in hindsight. Second, we want incentive compatibility, a guarantee that each expert's best strategy is to report his true beliefs about the realization of each event. To achieve this goal, we build on the literature on wagering mechanisms, a type of multi-agent scoring rul…
Efficient credit assignment is essential for reinforcement learning algorithms in both prediction and control settings. We describe a unified view on temporal-difference algorithms for selective credit assignment. These selective algorithms apply weightings to quantify the contribution of learning updates. We present insights into applying weightings to value-based learning and planning algorithms, and describe their role in mediating the backward credit distribution in prediction and control. Within this space, we identify some existing online learning algorithms that can assign credit select…
University of British Columbia（不列颠哥伦比亚大学）；Google（谷歌）
Prediction with experts' advice is one of the most fundamental problems in online learning and captures many of its technical challenges. A recent line of work has looked at online learning through the lens of differential equations and continuous-time analysis. This viewpoint has yielded optimal results for several problems in online learning. In this paper, we employ continuous-time stochastic calculus in order to study the discrete-time experts' problem. We use these tools to design a continuous-time, parameter-free algorithm with improved guarantees for the quantile regret. We then develop…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Tata Institute of Fundamental Research（塔塔基础研究院）
We consider the problem of estimating piecewise regular functions in an online setting, i.e., the data arrive sequentially and at any round our task is to predict the value of the true function at the next revealed point using the available data from past predictions. We propose a suitably modified version of a recently developed online learning algorithm called the sleeping experts aggregation algorithm. We show that this estimator satisfies oracle risk bounds simultaneously for all local regions of the domain. As concrete instantiations of the expert aggregation algorithm proposed here, we s…
We consider online learning problems in the realizable setting, where there is a zero-loss solution, and propose new Differentially Private (DP) algorithms that obtain near-optimal regret bounds. For the problem of online prediction from experts, we design new algorithms that obtain near-optimal regret ${O} \big( \varepsilon^{-1} \log^{1.5}{d} \big)$ where $d$ is the number of experts. This significantly improves over the best existing regret bounds for the DP non-realizable setting which are ${O} \big( \varepsilon^{-1} \min\big\{d, T^{1/3}\log d\big\} \big)$. We also develop an adaptive algor…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Ecole polytechnique fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Princeton University（普林斯顿大学）
We consider a learning system based on the conventional multiplicative weight (MW) rule that combines experts' advice to predict a sequence of true outcomes. It is assumed that one of the experts is malicious and aims to impose the maximum loss on the system. The loss of the system is naturally defined to be the aggregate absolute difference between the sequence of predicted outcomes and the true outcomes. We consider this problem under both offline and online settings. In the offline setting where the malicious expert must choose its entire sequence of decisions a priori, we show somewhat sur…
University of Science and Technology of China（中国科学技术大学）；Northwestern University（西北大学）；Princeton University（普林斯顿大学）
In generative adversarial imitation learning (GAIL), the agent aims to learn a policy from an expert demonstration so that its performance cannot be discriminated from the expert policy on a certain predefined reward set. In this paper, we study GAIL in both online and offline settings with linear function approximation, where both the transition and reward function are linear in the feature maps. Besides the expert demonstration, in the online setting the agent can interact with the environment, while in the offline setting the agent only accesses an additional dataset collected by a prior. F…
