We consider the problem of online learning where the sequence of actions played by the learner must adhere to an unknown safety constraint at every round. The goal is to minimize regret with respect to the best safe action in hindsight while simultaneously satisfying the safety constraint with high probability on each round. We provide a general meta-algorithm that leverages an online regression oracle to estimate the unknown safety constraint, and converts the predictions of an online learning oracle to predictions that adhere to the unknown safety constraint. On the theoretical side, our algorithm's regret can be bounded by the regret of the online regression and online learning oracles, the eluder dimension of the model class containing the unknown safety constraint, and a novel complexity measure that captures the difficulty of safe learning. We complement our result with an asymptotic lower bound that shows that the aforementioned complexity measure is necessary. When the constraints are linear, we instantiate our result to provide a concrete algorithm with $\sqrt{T}$ regret using a scaling transformation that balances optimistic exploration with pessimistic constraint satisfaction.
Simula Research Laboratory（西穆拉研究所）；LIRMM, University of Montpellier（蒙彼利埃大学计算机、机器人学与微电子学实验室）；CNRS（法国国家科学研究中心）
In most optimization problems, users have a clear understanding of the function to optimize (e.g., minimize the makespan for scheduling problems). However, the constraints may be difficult to state and their modelling often requires expertise in Constraint Programming. Active constraint acquisition has been successfully used to support non-experienced users in learning constraint networks through the generation of a sequence of queries. In this paper, we propose Learn&Optimize, a method to solve optimization problems with known objective function and unknown constraint network. It uses an acti…
Massachusetts Institute of Technology（麻省理工学院）；Princeton University（普林斯顿大学）
We study online learning in unknown Markov games, a problem that arises in episodic multi-agent reinforcement learning where the actions of the opponents are unobservable. We show that in this challenging setting, achieving sublinear regret against the best response in hindsight is statistically hard. We then consider a weaker notion of regret by competing with the \emph{minimax value} of the game, and present an algorithm that achieves a sublinear $\tilde{\mathcal{O}}(K^{2/3})$ regret after $K$ episodes. This is the first sublinear regret bound (to our knowledge) for online learning in unknow…
Tel Aviv University（特拉维夫大学）；Google Research（谷歌研究院）
We consider the problem of controlling an unknown linear dynamical system under a stochastic convex cost and full feedback of both the state and cost function. We present a computationally efficient algorithm that attains an optimal $\sqrt{T}$ regret-rate compared to the best stabilizing linear controller in hindsight. In contrast to previous work, our algorithm is based on the Optimism in the Face of Uncertainty paradigm. This results in a substantially improved computational complexity and a simpler analysis.
Solving Partially Observable Markov Decision Processes (POMDPs) is hard. Learning optimal controllers for POMDPs when the model is unknown is harder. Online learning of optimal controllers for unknown POMDPs, which requires efficient learning using regret-minimizing algorithms that effectively tradeoff exploration and exploitation, is even harder, and no solution exists currently. In this paper, we consider infinite-horizon average-cost POMDPs with unknown transition model, though a known observation model. We propose a natural posterior sampling-based reinforcement learning algorithm (PSRL-PO…
Student success models might be prone to develop weak spots, i.e., examples hard to accurately classify due to insufficient representation during model creation. This weakness is one of the main factors undermining users' trust, since model predictions could for instance lead an instructor to not intervene on a student in need. In this paper, we unveil the need of detecting and characterizing unknown unknowns in student success prediction in order to better understand when models may fail. Unknown unknowns include the students for which the model is highly confident in its predictions, but is …
This paper deals with bandit online learning problems involving feedback of unknown delay that can emerge in multi-armed bandit (MAB) and bandit convex optimization (BCO) settings. MAB and BCO require only values of the objective function involved that become available through feedback, and are used to estimate the gradient appearing in the corresponding iterative algorithms. Since the challenging case of feedback with \emph{unknown} delays prevents one from constructing the sought gradient estimates, existing MAB and BCO algorithms become intractable. For such challenging setups, delayed expl…
Israel Institute of Technology (Technion)（以色列理工学院）；ENSAE ParisTech（巴黎高等经济与统计学院）；GREGHEC: HEC Paris — CNRS（GREGHEC：巴黎高等商学院——法国国家科学研究中心）
In the standard setting of approachability there are two players and a target set. The players play repeatedly a known vector-valued game where the first player wants to have the average vector-valued payoff converge to the target set which the other player tries to exclude it from this set. We revisit this setting in the spirit of online learning and do not assume that the first player knows the game structure: she receives an arbitrary vector-valued reward vector at every round. She wishes to approach the smallest ("best") possible set given the observed average payoffs in hindsight. This ex…
We consider online learning when the time horizon is unknown. We apply a minimax analysis, beginning with the fixed horizon case, and then moving on to two unknown-horizon settings, one that assumes the horizon is chosen randomly according to some known distribution, and the other which allows the adversary full control over the horizon. For the random horizon setting with restricted losses, we derive a fully optimal minimax algorithm. And for the adversarial horizon setting, we prove a nontrivial lower bound which shows that the adversary obtains strictly more power than when the horizon is f…
Online optimization has recently opened avenues to study optimal control for time-varying cost functions that are unknown in advance. Inspired by this line of research, we study the distributed online linear quadratic regulator (LQR) problem for linear time-invariant (LTI) systems with unknown dynamics. Consider a multi-agent network where each agent is modeled as a LTI system. The network has a global time-varying quadratic cost, which may evolve adversarially and is only partially observed by each agent sequentially. The goal of the network is to collectively (i) estimate the unknown dynamic…
We consider the problem of online learning in the linear contextual bandits setting, but in which there are also strong individual fairness constraints governed by an unknown similarity metric. These constraints demand that we select similar actions or individuals with approximately equal probability (arXiv:1104.3913), which may be at odds with optimizing reward, thus modeling settings where profit and social policy are in tension. We assume we learn about an unknown Mahalanobis similarity metric from only weak feedback that identifies fairness violations, but does not quantify their extent. T…
We investigate the problem of online convex optimization with unknown delays, in which the feedback of a decision arrives with an arbitrary delay. Previous studies have presented a delayed variant of online gradient descent (OGD), and achieved the regret bound of $O(\sqrt{T+D})$ by only utilizing the convexity condition, where $D$ is the sum of delays over $T$ rounds. In this paper, we further exploit the strong convexity to improve the regret bound. Specifically, we first extend the delayed variant of OGD for strongly convex functions, and establish a better regret bound of $O(d\log T)$, wher…
Kernel-based methods exhibit well-documented performance in various nonlinear learning tasks. Most of them rely on a preselected kernel, whose prudent choice presumes task-specific prior information. Especially when the latter is not available, multi-kernel learning has gained popularity thanks to its flexibility in choosing kernels from a prescribed kernel dictionary. Leveraging the random feature approximation and its recent orthogonality-promoting variant, the present contribution develops a scalable multi-kernel learning scheme (termed Raker) to obtain the sought nonlinear learning functio…
Disentangling Long-Short Term State Under Unknown Interventions for Online Time Series Forecasting
School of Computer Science, Guangdong University of Technology（广东工业大学计算机学院）；Peng Cheng Laboratory（鹏城实验室）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Shantou University（汕头大学）
We study the problem of safe online convex optimization, where the action at each time step must satisfy a set of linear safety constraints. The goal is to select a sequence of actions to minimize the regret without violating the safety constraints at any time step (with high probability). The parameters that specify the linear safety constraints are unknown to the algorithm. The algorithm has access to only the noisy observations of constraints for the chosen actions. We propose an algorithm, called the {Safe Online Projected Gradient Descent} (SO-PGD) algorithm, to address this problem. We s…
Princeton University（普林斯顿大学）；Google AI Princeton（谷歌AI普林斯顿）；UC Berkeley（加州大学伯克利分校）；MIT（麻省理工学院）
We study online control of time-varying linear systems with unknown dynamics in the nonstochastic control model. At a high level, we demonstrate that this setting is \emph{qualitatively harder} than that of either unknown time-invariant or known time-varying dynamics, and complement our negative results with algorithmic upper bounds in regimes where sublinear regret is possible. More specifically, we study regret bounds with respect to common classes of policies: Disturbance Action (SLS), Disturbance Response (Youla), and linear feedback policies. While these three classes are essentially equi…
Università dell’Insubria（因苏布里亚大学）；University College London（伦敦大学学院）
We consider online similarity prediction problems over networked data. We begin by relating this task to the more standard class prediction problem, showing that, given an arbitrary algorithm for class prediction, we can construct an algorithm for similarity prediction with "nearly" the same mistake bound, and vice versa. After noticing that this general construction is computationally infeasible, we target our study to {\em feasible} similarity prediction algorithms on networked data. We initially assume that the network structure is {\em known} to the learner. Here we observe that Matrix Win…
University of Maryland, College Park（马里兰大学帕克分校）；Shanghai Jiao Tong University（上海交通大学）
Poisoning attacks on Reinforcement Learning (RL) systems could take advantage of RL algorithm's vulnerabilities and cause failure of the learning. However, prior works on poisoning RL usually either unrealistically assume the attacker knows the underlying Markov Decision Process (MDP), or directly apply the poisoning methods in supervised learning to RL. In this work, we build a generic poisoning framework for online RL via a comprehensive investigation of heterogeneous poisoning models in RL. Without any prior knowledge of the MDP, we propose a strategic poisoning algorithm called Vulnerabili…
Technische Universität Darmstadt（达姆施塔特工业大学）；Max-Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Universität zu Lübeck（吕贝克大学）
Autonomous robots need to interact with unknown, unstructured and changing environments, constantly facing novel challenges. Therefore, continuous online adaptation for lifelong-learning and the need of sample-efficient mechanisms to adapt to changes in the environment, the constraints, the tasks, or the robot itself are crucial. In this work, we propose a novel framework for probabilistic online motion planning with online adaptation based on a bio-inspired stochastic recurrent neural network. By using learning signals which mimic the intrinsic motivation signalcognitive dissonance in additio…
The growing prospect of deep reinforcement learning (DRL) being used in cyber-physical systems has raised concerns around safety and robustness of autonomous agents. Recent work on generating adversarial attacks have shown that it is computationally feasible for a bad actor to fool a DRL policy into behaving sub optimally. Although certain adversarial attacks with specific attack models have been addressed, most studies are only interested in off-line optimization in the data space (e.g., example fitting, distillation). This paper introduces a Meta-Learned Advantage Hierarchy (MLAH) framework …
Online Learning for Dynamic Vickrey-Clarke-Groves Mechanism in Unknown Environments
Department of Industrial \& Enterprise Systems Engineering；Coordinated Science Laboratory, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA；Department of Industrial \& Enterprise Systems Engineering, Department of Electrical \& Computer Engineering
We consider online optimization in the 1-lookahead setting, where the objective does not decompose additively over the rounds of the online game. The resulting formulation enables us to deal with non-stationary and/or long-term constraints , which arise, for example, in online display advertising problems. We propose an on-line primal-dual algorithm for which we obtain dynamic cumulative regret guarantees. They depend on the convexity and the smoothness of the non-additive penalty, as well as terms capturing the smoothness with which the residuals of the non-stationary and long-term constraint…
We consider the problem of online learning in the presence of distribution shifts that occur at an unknown rate and of unknown intensity. We derive a new Bayesian online inference approach to simultaneously infer these distribution shifts and adapt the model to the detected changes by integrating ideas from change point detection, switching dynamical systems, and Bayesian online learning. Using a binary 'change variable,' we construct an informative prior such that--if a change is detected--the model partially erases the information of past model updates by tempering to facilitate adaptation t…
Norwegian University of Science and Technology（挪威科技大学）
Despite the recent success of artificial neural networks, more biologically plausible learning methods may be needed to resolve the weaknesses of backpropagation trained models such as catastrophic forgetting and adversarial attacks. Although these weaknesses are not specifically addressed, a novel local learning rule is presented that performs online clustering with an upper limit on the number of clusters to be found rather than a fixed cluster count. Instead of using orthogonal weight or output activation constraints, activation sparsity is achieved by mutual repulsion of lateral Gaussian n…
With the dawn of the Big Data era, data sets are growing rapidly. Data is streaming from everywhere - from cameras, mobile phones, cars, and other electronic devices. Clustering streaming data is a very challenging problem. Unlike the traditional clustering algorithms where the dataset can be stored and scanned multiple times, clustering streaming data has to satisfy constraints such as limit memory size, real-time response, unknown data statistics and an unknown number of clusters. In this paper, we present a novel online clustering algorithm which can be used to cluster streaming data withou…
National University of Defense Technology（国防科技大学）；Jilin University（吉林大学）
Robust model predictive control (MPC) is a well-known control technique for model-based control with constraints and uncertainties. In classic robust tube-based MPC approaches, an open-loop control sequence is computed via periodically solving an online nominal MPC problem, which requires prior model information and frequent access to onboard computational resources. In this paper, we propose an efficient robust MPC solution based on receding horizon reinforcement learning, called r-LPC, for unknown nonlinear systems with state constraints and disturbances. The proposed r-LPC utilizes a Koopma…
Online optimization with multiple budget constraints is challenging since the online decisions over a short time horizon are coupled together by strict inventory constraints. The existing manually-designed algorithms cannot achieve satisfactory average performance for this setting because they often need a large number of time steps for convergence and/or may violate the inventory constraints. In this paper, we propose a new machine learning (ML) assisted unrolling approach, called LAAU (Learning-Assisted Algorithm Unrolling), which unrolls the online decision pipeline and leverages an ML mode…
Nanjing University（南京大学）；the University of Iowa（爱荷华大学）；Michigan State University（密歇根州立大学）
In this paper, we study a special bandit setting of online stochastic linear optimization, where only one-bit of information is revealed to the learner at each round. This problem has found many applications including online advertisement and online recommendation. We assume the binary feedback is a random variable generated from the logit model, and aim to minimize the regret defined by the unknown linear function. Although the existing method for generalized linear bandit can be applied to our problem, the high computational cost makes it impractical for real-world problems. To address this …
In this paper, we consider the problem of predicting observations generated online by an unknown, partially observed linear system, which is driven by stochastic noise. For such systems the optimal predictor in the mean square sense is the celebrated Kalman filter, which can be explicitly computed when the system model is known. When the system model is unknown, we have to learn how to predict observations online based on finite data, suffering possibly a non-zero regret with respect to the Kalman filter's prediction. We show that it is possible to achieve a regret of the order of $\mathrm{pol…
Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this paper, we study Bayesian optimization for constrained problems in the general case that noise may be present in the constraint functions, and the objective and constraints may be evaluated independently. We provide motivating practical examples, and present a general framework to solve such problems. We demonstrate the effectiveness of our approach on optimi…
Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）；New York University（纽约大学）
Reinforcement learning algorithms have had tremendous successes in online learning settings. However, these successes have relied on low-stakes interactions between the algorithmic agent and its environment. In many settings where RL could be of use, such as health care and autonomous driving, the mistakes made by most online RL algorithms during early training come with unacceptable costs. These settings require developing reinforcement learning algorithms that can operate in the so-called batch setting, where the algorithms must learn from set of data that is fixed, finite, and generated fro…
ShanghaiTech University（上海科技大学）；University of Michigan, Ann Arbor（密歇根大学安娜堡分校）
This paper studies online nonstochastic control problems with adversarial and static constraints. We propose online nonstochastic control algorithms that achieve both sublinear regret and sublinear adversarial constraint violation while keeping static constraint violation minimal against the optimal constrained linear control policy in hindsight. To establish the results, we introduce an online convex optimization with memory framework under adversarial and static constraints, which serves as a subroutine for the constrained online nonstochastic control algorithms. This subroutine also achieve…
Online Learning for Optimizing AoI-Energy Tradeoff under Unknown Channel Statistics
Department of ECE The Ohio State University（电子工程系 奥地大学）；Department of EE University at Buffalo（电气工程系 伯克利大学）；CSE The Ohio State University（计算科学与工程系 奥地大学）
Regret minimization has proved to be a versatile tool for tree-form sequential decision making and extensive-form games. In large two-player zero-sum imperfect-information games, modern extensions of counterfactual regret minimization (CFR) are currently the practical state of the art for computing a Nash equilibrium. Most regret-minimization algorithms for tree-form sequential decision making, including CFR, require (i) an exact model of the player's decision nodes, observation nodes, and how they are linked, and (ii) full knowledge, at all times t, about the payoffs -- even in parts of the d…
This paper analyzes DONE, an online optimization algorithm that iteratively minimizes an unknown function based on costly and noisy measurements. The algorithm maintains a surrogate of the unknown function in the form of a random Fourier expansion (RFE). The surrogate is updated whenever a new measurement is available, and then used to determine the next measurement point. The algorithm is comparable to Bayesian optimization algorithms, but its computational complexity per iteration does not depend on the number of measurements. We derive several theoretical results that provide insight on how…
In this paper we formulate the nonnegative matrix factorisation (NMF) problem as a maximum likelihood estimation problem for hidden Markov models and propose online expectation-maximisation (EM) algorithms to estimate the NMF and the other unknown static parameters. We also propose a sequential Monte Carlo approximation of our online EM algorithm. We show the performance of the proposed method with two numerical examples.
University of Michigan, Ann Arbor（密歇根大学安娜堡分校）；University of Rhode Island（罗德岛大学）；Purdue University（普渡大学）
This paper considers constrained online dispatching with unknown arrival, reward and constraint distributions. We propose a novel online dispatching algorithm, named POND, standing for Pessimistic-Optimistic oNline Dispatching, which achieves $O(\sqrt{T})$ regret and $O(1)$ constraint violation. Both bounds are sharp. Our experiments on synthetic and real datasets show that POND achieves low regret with minimal constraint violations.
MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）；University of Padova（帕多瓦大学）
AI systems that learn through reward feedback about the actions they take are increasingly deployed in domains that have significant impact on our daily life. However, in many cases the online rewards should not be the only guiding criteria, as there are additional constraints and/or priorities imposed by regulations, values, preferences, or ethical principles. We detail a novel online agent that learns a set of behavioral constraints by observation and uses these learned constraints as a guide when making decisions in an online setting while still being reactive to reward feedback. To define …
Motivated by e-commerce, we study the online assortment optimization problem. The seller offers an assortment, i.e. a subset of products, to each arriving customer, who then purchases one or no product from her offered assortment. A customer's purchase decision is governed by the underlying MultiNomial Logit (MNL) choice model. The seller aims to maximize the total revenue in a finite sales horizon, subject to resource constraints and uncertainty in the MNL choice model. We first propose an efficient online policy which incurs a regret $\tilde{O}(T^{2/3})$, where $T$ is the number of customers…
In this paper, we consider online continuous DR-submodular maximization with linear stochastic long-term constraints. Compared to the prior work on online submodular maximization, our setting introduces the extra complication of stochastic linear constraint functions that are i.i.d. generated at each round. To be precise, at step $t\in\{1,\dots,T\}$, a DR-submodular utility function $f_t(\cdot)$ and a constraint vector $p_t$, i.i.d. generated from an unknown distribution with mean $p$, are revealed after committing to an action $x_t$ and we aim to maximize the overall utility while the expecte…
Online Learning and Optimization for Queues with Unknown Demand Curve and Service Distribution
School of Data Science, School of Management and Economics, Chinese University of Hong Kong (Shenzhen)（数据科学学院、管理与经济学学院、香港中文大学（深圳））；College of Business, Shanghai University of Finance and Economics（财经大学商学院）；Dept. of Industrial and Systems Engineering, North Carolina State University（工业与系统工程系、北卡罗来纳州立大学）
University of Washington（华盛顿大学）；Microsoft Research NYC（微软研究院纽约）
This work studies the problem of sequential control in an unknown, nonlinear dynamical system, where we model the underlying system dynamics as an unknown function in a known Reproducing Kernel Hilbert Space. This framework yields a general setting that permits discrete and continuous control inputs as well as non-smooth, non-differentiable dynamics. Our main result, the Lower Confidence-based Continuous Control ($LC^3$) algorithm, enjoys a near-optimal $O(\sqrt{T})$ regret bound against the optimal controller in episodic settings, where $T$ is the number of episodes. The bound has no explicit…
University of California Irvine（加州大学欧文分校）；Expedia Group（亿客行集团）
In this paper, we investigate the framework of Online Convex Optimization (OCO) for online learning. OCO offers a very powerful online learning framework for many applications. In this context, we study a specific framework of OCO called {\it OCO with long term constraints}. Long term constraints are introduced typically as an alternative to reduce the complexity of the projection at every update step in online optimization. While many algorithmic advances have been made towards online optimization with long term constraints, these algorithms typically assume that the sequence of cost function…
We study algorithms for online linear optimization in Hilbert spaces, focusing on the case where the player is unconstrained. We develop a novel characterization of a large class of minimax algorithms, recovering, and even improving, several previous results as immediate corollaries. Moreover, using our tools, we develop an algorithm that provides a regret bound of $\mathcal{O}\Big(U \sqrt{T \log(U \sqrt{T} \log^2 T +1)}\Big)$, where $U$ is the $L_2$ norm of an arbitrary comparator and both $T$ and $U$ are unknown to the player. This bound is optimal up to $\sqrt{\log \log T}$ terms. When $T$ …
