We consider a variant of the classical online linear optimization problem in which at every step, the online player receives a "hint" vector before choosing the action for that round. Rather surprisingly, it was shown that if the hint vector is guaranteed to have a positive correlation with the cost vector, then the online player can achieve a regret of $O(\log T)$, thus significantly improving over the $O(\sqrt{T})$ regret in the general setting. However, the result and analysis require the correlation property at \emph{all} time steps, thus raising the natural question: can we design online learning algorithms that are resilient to bad hints?
In this paper we develop algorithms and nearly matching lower bounds for online learning with imperfect directional hints. Our algorithms are oblivious to the quality of the hints, and the regret bounds interpolate between the always-correlated hints case and the no-hints case. Our results also generalize, simplify, and improve upon previous results on optimistic regret bounds, which can be viewed as an additive version of hints.
We provide algorithms that guarantee regret $R_T(u)\le \tilde O(G\|u\|^3 + G(\|u\|+1)\sqrt{T})$ or $R_T(u)\le \tilde O(G\|u\|^3T^{1/3} + GT^{1/3}+ G\|u\|\sqrt{T})$ for online convex optimization with $G$-Lipschitz losses for any comparison point $u$ without prior knowledge of either $G$ or $\|u\|$. Previous algorithms dispense with the $O(\|u\|^3)$ term at the expense of knowledge of one or both of these parameters, while a lower bound shows that some additional penalty term over $G\|u\|\sqrt{T}$ is necessary. Previous penalties were exponential while our bounds are polynomial in all quantitie…
Criteo AI Lab（Criteo人工智能实验室）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；LIG（格勒诺布尔信息学实验室）
We consider the problem of online learning with non-convex losses. In terms of feedback, we assume that the learner observes - or otherwise constructs - an inexact model for the loss function encountered at each stage, and we propose a mixed-strategy learning policy based on dual averaging. In this general context, we derive a series of tight regret minimization guarantees, both for the learner's static (external) regret, as well as the regret incurred against the best dynamic policy in hindsight. Subsequently, we apply this general template to the case where the learner only has access to the…
University of Utah（犹他大学）；Google Research（谷歌研究院）；Duke University（杜克大学）
We consider the classic online learning and stochastic multi-armed bandit (MAB) problems, when at each step, the online policy can probe and find out which of a small number ($k$) of choices has better reward (or loss) before making its choice. In this model, we derive algorithms whose regret bounds have exponentially better dependence on the time horizon compared to the classic regret bounds. In particular, we show that probing with $k=2$ suffices to achieve time-independent regret bounds for online linear and convex optimization. The same number of probes improve the regret bound of stochast…
University of Utah（犹他大学）；Boston University（波士顿大学）；Google Research（谷歌研究院）
We consider the online linear optimization problem, where at every step the algorithm plays a point $x_t$ in the unit ball, and suffers loss $\langle c_t, x_t\rangle$ for some cost vector $c_t$ that is then revealed to the algorithm. Recent work showed that if an algorithm receives a hint $h_t$ that has non-trivial correlation with $c_t$ before it plays $x_t$, then it can achieve a regret guarantee of $O(\log T)$, improving on the bound of $Θ(\sqrt{T})$ in the standard setting. In this work, we study the question of whether an algorithm really requires a hint at every time step. Somewhat surpr…
The Australian National University（澳大利亚国立大学）；Data61；Centrum Wiskunde & Informatica（数学和计算机科学中心）
We study Online Convex Optimization in the unbounded setting where neither predictions nor gradient are constrained. The goal is to simultaneously adapt to both the sequence of gradients and the comparator. We first develop parameter-free and scale-free algorithms for a simplified setting with hints. We present two versions: the first adapts to the squared norms of both comparator and gradients separately using $O(d)$ time per round, the second adapts to their squared inner products (which measure variance only in the comparator direction) in time $O(d^3)$ per round. We then generalize two pri…
In this paper, we study oracle-efficient algorithms for beyond worst-case analysis of online learning. We focus on two settings. First, the smoothed analysis setting of [RST11,HRS22] where an adversary is constrained to generating samples from distributions whose density is upper bounded by $1/σ$ times the uniform density. Second, the setting of $K$-hint transductive learning, where the learner is given access to $K$ hints per time step that are guaranteed to include the true instance. We give the first known oracle-efficient algorithms for both settings that depend only on the pseudo (or VC) …
With the advent and increasing consolidation of e-commerce, digital advertising has very recently replaced traditional advertising as the main marketing force in the economy. In the past four years, a particularly important development in the digital advertising industry is the shift from second-price auctions to first-price auctions for online display ads. This shift immediately motivated the intellectually challenging question of how to bid in first-price auctions, because unlike in second-price auctions, bidding one's private value truthfully is no longer optimal. Following a series of rece…
University of Utah（犹他大学）；Google Research（谷歌研究院）；Boston University（波士顿大学）
We study an online linear optimization (OLO) problem in which the learner is provided access to $K$ "hint" vectors in each round prior to making a decision. In this setting, we devise an algorithm that obtains logarithmic regret whenever there exists a convex combination of the $K$ hints that has positive correlation with the cost vectors. This significantly extends prior work that considered only the case $K=1$. To accomplish this, we develop a way to combine many arbitrary OLO algorithms to obtain regret only a logarithmically worse factor than the minimum regret of the original algorithms i…
Smoothed online combinatorial optimization considers a learner who repeatedly chooses a combinatorial decision to minimize an unknown changing cost function with a penalty on switching decisions in consecutive rounds. We study smoothed online combinatorial optimization problems when an imperfect predictive model is available, where the model can forecast the future cost functions with uncertainty. We show that using predictions to plan for a finite time horizon leads to regret dependent on the total predictive uncertainty and an additional switching cost. This observation suggests choosing a s…
The current state of the art in playing many important perfect information games, including Chess and Go, combines planning and deep reinforcement learning with self-play. We extend this approach to imperfect information games and present ExIt-OOS, a novel approach to playing imperfect information games within the Expert Iteration framework and inspired by AlphaZero. We use Online Outcome Sampling, an online search algorithm for imperfect information games in place of MCTS. While training online, our neural strategy is used to improve the accuracy of playouts in OOS, allowing a learning and pl…
Massachusetts Institute of Technology（麻省理工学院）；Woods Hole Oceanographic Institution（伍兹霍尔海洋研究所）；Boston University（波士顿大学）；Atmospheric and Environmental Research（大气与环境研究公司）；University of Toronto（多伦多大学）；Microsoft Research New England（微软新英格兰研究院）；Instituto de Matemática Pura e Aplicada（纯数学与应用数学研究所）
Inspired by the demands of real-time climate and weather forecasting, we develop optimistic online learning algorithms that require no parameter tuning and have optimal regret guarantees under delayed feedback. Our algorithms -- DORM, DORM+, and AdaHedgeD -- arise from a novel reduction of delayed online learning to optimistic online learning that reveals how optimistic hints can mitigate the regret penalty caused by delay. We pair this delay-as-optimism perspective with a new analysis of optimistic learning that exposes its robustness to hinting errors and a new meta-algorithm for learning ef…
Industrial Engineering and Operations Research, Columbia University（哥伦比亚大学工业工程与运筹学系）；School of Computing, National University of Singapore（新加坡国立大学计算机学院）
A burgeoning paradigm in algorithm design is the field of algorithms with predictions, in which algorithms can take advantage of a possibly-imperfect prediction of some aspect of the problem. While much work has focused on using predictions to improve competitive ratios, running times, or other performance measures, less effort has been devoted to the question of how to obtain the predictions themselves, especially in the critical online setting. We introduce a general design approach for algorithms that learn predictors: (1) identify a functional dependence of the performance measure on the p…
Guarded Policy Optimization with Imperfect Online Demonstrations
Nanyang Technological University（南洋理工大学）；University of California, Los Angeles（加州大学洛杉矶分校）；The University of Edinburgh（爱丁堡大学）；Northwestern University（西北大学）
Tsinghua University（清华大学）；University of Science & Technology Beijing（北京科技大学）
Pretraining reinforcement learning methods with demonstrations has been an important concept in the study of reinforcement learning since a large amount of computing power is spent on online simulations with existing reinforcement learning algorithms. Pretraining reinforcement learning remains a significant challenge in exploiting expert demonstrations whilst keeping exploration potentials, especially for value based methods. In this paper, we propose a pretraining method for soft Q-learning. Our work is inspired by pretraining methods for actor-critic algorithms since soft Q-learning is a val…
Reward function is essential in reinforcement learning (RL), serving as the guiding signal to incentivize agents to solve given tasks, however, is also notoriously difficult to design. In many cases, only imperfect rewards are available, which inflicts substantial performance loss for RL agents. In this study, we propose a unified offline policy optimization approach, \textit{RGM (Reward Gap Minimization)}, which can smartly handle diverse types of imperfect rewards. RGM is formulated as a bi-level optimization problem: the upper layer optimizes a reward correction term that performs visitatio…
Reinforcement Learning with Imperfect Transition Predictions: A Bellman-Jensen Approach
Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Edwardson School of Industrial Engineering, Purdue University（普渡大学爱德华森工业工程学院）；School of Data Science, The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳）数据科学学院）；School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳）理工学院）；Computing & Mathematical Sciences, Caltech（加州理工学院计算与数学科学系）
A standard assumption in contextual multi-arm bandit is that the true context is perfectly known before arm selection. Nonetheless, in many practical applications (e.g., cloud resource management), prior to arm selection, the context information can only be acquired by prediction subject to errors or adversarial modification. In this paper, we study a contextual bandit setting in which only imperfect context is available for arm selection while the true context is revealed at the end of each round. We propose two robust arm selection algorithms: MaxMinUCB (Maximize Minimum UCB) which maximizes…
When to Trust Your Simulator: Dynamics-Aware Hybrid Offline-and-Online Reinforcement Learning
Tsinghua University（清华大学）；Indian Institute of Technology（印度理工学院）；Shanghai Jiaotong University（上海交通大学）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；Shanghai AI Laboratory（上海人工智能实验室）
We consider online algorithms for the {\em page migration problem} that use predictions, potentially imperfect, to improve their performance. The best known online algorithms for this problem, due to Westbrook'94 and Bienkowski et al'17, have competitive ratios strictly bounded away from 1. In contrast, we show that if the algorithm is given a prediction of the input sequence, then it can achieve a competitive ratio that tends to $1$ as the prediction error rate tends to $0$. Specifically, the competitive ratio is equal to $1+O(q)$, where $q$ is the prediction error rate. We also design a ``fa…
Minimizing Weighted Counterfactual Regret with Optimistic Online Mirror Descent
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；Tencent AI Lab（腾讯AI实验室）；Tsinghua University（清华大学）；School of Future Technology, University of Chinese Academy of Sciences（中国科学院大学未来技术学院）
University of Trento（特伦托大学）；Aarhus University（奥胡斯大学）
We introduce Explearn, an online algorithm that learns to jointly output predictions and explanations for those predictions. Explearn leverages Gaussian Processes (GP)-based contextual bandits. This brings two key benefits. First, GPs naturally capture different kinds of explanations and enable the system designer to control how explanations generalize across the space by virtue of choosing a suitable kernel. Second, Explearn builds on recent results in contextual bandits which guarantee convergence with high probability. Our initial experiments hint at the promise of the approach.
Improved Bounds for Online Facility Location with Predictions
National Technical University of Athens（雅典国立技术大学）；Archimedes/Athena RC（阿基米德/雅典娜研究中心）；University of Wisconsin - Madison（威斯康星大学麦迪逊分校）；National University of Singapore（新加坡国立大学）；University of California, Irvine（加州大学欧文分校）
Indian Institute of Technology Madras（印度理工学院马德拉斯分校）；Chennai Mathematical Institute（金奈数学研究所）；Indian Institute of Technology (ISM) Dhanbad（印度理工学院（印度矿业学院）丹巴德分校）；Tata Institute of Fundamental Research（塔塔基础研究所）
We revisit the classic problem of optimal subset selection in the online learning set-up. Assume that the set $[N]$ consists of $N$ distinct elements. On the $t$th round, an adversary chooses a monotone reward function $f_t: 2^{[N]} \to \mathbb{R}_+$ that assigns a non-negative reward to each subset of $[N].$ An online policy selects (perhaps randomly) a subset $S_t \subseteq [N]$ consisting of $k$ elements before the reward function $f_t$ for the $t$th round is revealed to the learner. As a consequence of its choice, the policy receives a reward of $f_t(S_t)$ on the $t$th round. Our goal is t…
There is significant interest in deploying machine learning algorithms for diagnostic radiology, as modern learning techniques have made it possible to detect abnormalities in medical images within minutes. While machine-assisted diagnoses cannot yet reliably replace human reviews of images by a radiologist, they could inform prioritization rules for determining the order by which to review patient cases so that patients with time-sensitive conditions could benefit from early intervention. We study this scenario by formulating it as a learning-augmented online scheduling problem. We are given …
