This paper presents competitive algorithms for a novel class of online optimization problems with memory. We consider a setting where the learner seeks to minimize the sum of a hitting cost and a switching cost that depends on the previous $p$ decisions. This setting generalizes Smoothed Online Convex Optimization. The proposed approach, Optimistic Regularized Online Balanced Descent, achieves a constant, dimension-free competitive ratio. Further, we show a connection between online optimization with memory and online control with adversarial disturbances. This connection, in turn, leads to a new constant-competitive policy for a rich class of online control problems.
California Institute of Technology（加州理工学院）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）
We study online convex optimization in a setting where the learner seeks to minimize the sum of a per-round hitting cost and a movement cost which is incurred when changing decisions between rounds. We prove a new lower bound on the competitive ratio of any online algorithm in the setting where the costs are $m$-strongly convex and the movement costs are the squared $\ell_2$ norm. This lower bound shows that no algorithm can achieve a competitive ratio that is $o(m^{-1/2})$ as $m$ tends to zero. No existing algorithms have competitive ratios matching this bound, and we show that the state-of-t…
We consider Online Convex Optimization (OCO) in the setting where the costs are $m$-strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced Descent (OBD) algorithm is constant competitive in this setting, with competitive ratio $3 + O(1/m)$, irrespective of the ambient dimension. Additionally, we show that when the sequence of cost functions is $ε$-smooth, OBD has near-optimal dynamic regret and maintains strong per-round accuracy. We demonstrate the generality of our approach by showing that the OBD…
The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；Google Research（谷歌研究院）；Tel Aviv University（特拉维夫大学）
We consider online algorithms under both the competitive ratio criteria and the regret minimization one. Our main goal is to build a unified methodology that would be able to guarantee both criteria simultaneously. For a general class of online algorithms, namely any Metrical Task System (MTS), we show that one can simultaneously guarantee the best known competitive ratio and a natural regret bound. For the paging problem we further show an efficient online algorithm (polynomial in the number of pages) with this guarantee. To this end, we extend an existing regret minimization algorithm (speci…
We consider the problem of tracking an adversarial state sequence in a linear dynamical system subject to adversarial disturbances and loss functions, generalizing earlier settings in the literature. To this end, we develop three techniques, each of independent interest. First, we propose a comparator-adaptive algorithm for online linear optimization with movement cost. Without tuning, it nearly matches the performance of the optimally tuned gradient descent in hindsight. Next, considering a related problem called online learning with memory, we construct a novel strongly adaptive algorithm th…
IIIS, Tsinghua University（清华大学交叉信息研究院）；California Institute of Technology（加州理工学院）
We study online optimization in a setting where an online learner seeks to optimize a per-round hitting cost, which may be non-convex, while incurring a movement cost when changing actions between rounds. We ask: \textit{under what general conditions is it possible for an online learner to leverage predictions of future cost functions in order to achieve near-optimal costs?} Prior work has provided near-optimal online algorithms for specific combinations of assumptions about hitting and switching costs, but no general results are known. In this work, we give two general sufficient conditions t…
The framework of online learning with memory naturally captures learning problems with temporal constraints, and was previously studied for the experts setting. In this work we extend the notion of learning with memory to the general Online Convex Optimization (OCO) framework, and present two algorithms that attain low regret. The first algorithm applies to Lipschitz continuous loss functions, obtaining optimal regret bounds for both convex and strongly convex losses. The second algorithm attains the optimal regret bounds and applies more broadly to convex losses without requiring Lipschitz co…
University of Washington（华盛顿大学）；Tetration Analytics, Cisco Systems, Inc.（思科系统公司Tetration Analytics部门）
In this paper, we study a certain class of online optimization problems, where the goal is to maximize a function that is not necessarily concave and satisfies the Diminishing Returns (DR) property under budget constraints. We analyze a primal-dual algorithm, called the Generalized Sequential algorithm, and we obtain the first bound on the competitive ratio of online monotone DR-submodular function maximization subject to linear packing constraints which matches the known tight bound in the special case of linear objective function.
Simons Institute, UC Berkeley（加州大学伯克利分校西蒙斯研究所）；Google AI Princeton（谷歌人工智能普林斯顿团队）；Tepper School of Business, Carnegie Mellon University（卡内基梅隆大学泰珀商学院）；Department of Computer Science, Princeton University（普林斯顿大学计算机科学系）
We consider the fundamental problem of online control of a linear dynamical system from two different viewpoints: regret minimization and competitive analysis. We prove that the optimal competitive policy is well-approximated by a convex parameterized policy class, known as a disturbance-action control (DAC) policies. Using this structural result, we show that several recently proposed online control algorithms achieve the best of both worlds: sublinear regret vs. the best DAC policy selected in hindsight, and optimal competitive ratio, up to an additive correction which grows sublinearly in t…
We study the problem of online resource allocation, where multiple customers arrive sequentially and the seller must irrevocably allocate resources to each incoming customer while also facing a procurement cost for the total allocation. Assuming resource procurement follows an a priori known marginally increasing cost function, the objective is to maximize the reward obtained from fulfilling the customers' requests sans the cumulative procurement cost. We analyze the competitive ratio of a primal-dual algorithm in this setting, and develop an optimization framework for synthesizing a surrogate…
In this article, we propose a novel form of unsupervised learning, continual competitive memory (CCM), as well as a computational framework to unify related neural models that operate under the principles of competition. The resulting neural system is shown to offer an effective approach for combating catastrophic forgetting in online continual classification problems. We demonstrate that the proposed CCM system not only outperforms other competitive learning neural models but also yields performance that is competitive with several modern, state-of-the-art lifelong learning approaches on benc…
Machine learning algorithms are designed to make accurate predictions of the future based on existing data, while online algorithms seek to bound some performance measure (typically the competitive ratio) without knowledge of the future. Lykouris and Vassilvitskii demonstrated that augmenting online algorithms with a machine learned predictor can provably decrease the competitive ratio under as long as the predictor is suitably accurate. In this work we apply this idea to the Online Metrical Task System problem, which was put forth by Borodin, Linial, and Saks as a general model for dynamic sy…
Carnegie Mellon University（卡内基梅隆大学）；The Chinese University of Hong Kong（香港中文大学）；Microsoft Research（微软研究院）
Online influence maximization has attracted much attention as a way to maximize influence spread through a social network while learning the values of unknown network parameters. Most previous works focus on single-item diffusion. In this paper, we introduce a new Online Competitive Influence Maximization (OCIM) problem, where two competing items (e.g., products, news stories) propagate in the same network and influence probabilities on edges are unknown. We adopt a combinatorial multi-armed bandit (CMAB) framework for OCIM, but unlike the non-competitive setting, the important monotonicity pr…
The online assignment problem plays an important role in operational research and computer science which is why immense attention has been given to improving its solution quality. Due to the incomplete information about the input, it is difficult for online algorithms to produce the optimal solution. The quality of the solution of an online algorithm is measured using a competitive ratio. No online deterministic algorithm can achieve a competitive ratio better than (2n-1). It has been shown that advice in online computation improves the lower bound of the competitive ratio of online problems. …
DeepMind（深度思维）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Google Brain（谷歌大脑）；Baidu Apollo（百度阿波罗）
A challenging problem in task-free continual learning is the online selection of a representative replay memory from data streams. In this work, we investigate the online memory selection problem from an information-theoretic perspective. To gather the most information, we propose the \textit{surprise} and the \textit{learnability} criteria to pick informative points and to avoid outliers. We present a Bayesian model to compute the criteria efficiently by exploiting rank-one matrix structures. We demonstrate that these criteria encourage selecting informative points in a greedy algorithm for o…
Augmenting a neural network with memory that can grow without growing the number of trained parameters is a recent powerful concept with many exciting applications. We propose a design of memory augmented neural networks (MANNs) called Labeled Memory Networks (LMNs) suited for tasks requiring online adaptation in classification models. LMNs organize the memory with classes as the primary key.The memory acts as a second boosted stage following a regular neural network thereby allowing the memory and the primary network to play complementary roles. Unlike existing MANNs that write to memory for …
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…
Online continual learning, especially when task identities and task boundaries are unavailable, is a challenging continual learning setting. One representative kind of methods for online continual learning is replay-based methods, in which a replay buffer called memory is maintained to keep a small part of past samples for overcoming catastrophic forgetting. When tackling with online continual learning, most existing replay-based methods focus on single-label problems in which each sample in the data stream has only one label. But multi-label problems may also happen in the online continual le…
Competitive online games use rating systems for matchmaking; progression-based algorithms that estimate the skill level of players with interpretable ratings in terms of the outcome of the games they played. However, the overall experience of players is shaped by factors beyond the sole outcome of their games. In this paper, we engineer several features from in-game statistics to model players and create ratings that accurately represent their behavior and true performance level. We then compare the estimating power of our behavioral ratings against ratings created with three mainstream rating…
Competitive online games use rating systems to match players with similar skills to ensure a satisfying experience for players. In this paper, we focus on the importance of addressing different aspects of playing behavior when modeling players for creating match-ups. To this end, we engineer several behavioral features from a dataset of over 75,000 battle royale matches and create player models based on the retrieved features. We then use the created models to predict ranks for different groups of players in the data. The predicted ranks are compared to those of three popular rating systems. O…
Università degli Studi di Milano（米兰大学）；Toulouse School of Economics（图卢兹经济学院）；CLC Space GmbH（CLC航天有限公司）；Politecnico di Milano（米兰理工大学）
In this paper, we present a real-world application of online learning with expert advice to the field of Space Operations, testing our theory on real-life data coming from the Copernicus Sentinel-6 satellite. We show that in Spacecraft Memory Dump Optimization, a lightweight Follow-The-Leader algorithm leads to an increase in performance of over $60\%$ when compared to traditional techniques.
The Hong Kong University of Science and Technology（香港科技大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；California Institute of Technology（加州理工学院）
This paper leverages machine-learned predictions to design competitive algorithms for online conversion problems with the goal of improving the competitive ratio when predictions are accurate (i.e., consistency), while also guaranteeing a worst-case competitive ratio regardless of the prediction quality (i.e., robustness). We unify the algorithmic design of both integral and fractional conversion problems, which are also known as the 1-max-search and one-way trading problems, into a class of online threshold-based algorithms (OTA). By incorporating predictions into design of OTA, we achieve th…
School of Mathematics, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所数学学院（IPM））
Working Memory is the brain module that holds and manipulates information online. In this work, we design a hybrid model in which a simple feed-forward network is coupled to a balanced random network via a read-write vector called the interface vector. Three cases and their results are discussed similar to the n-back task called, first-order memory binding task, generalized first-order memory task, and second-order memory binding task. The important result is that our dual-component model of working memory shows good performance with learning restricted to the feed-forward component only. Here…
