ICML 2023 Papers

We study the problem of online learning in a two-player decentralized cooperative Stackelberg game. In each round, the leader first takes an action, followed by the follower who takes their action after observing the leader's move. The goal of the leader is to learn to minimize the cumulative regret based on the history of interactions. Differing from the traditional formulation of repeated Stackelberg games, we assume the follower is omniscient, with full knowledge of the true reward, and that they always best-respond to the leader's actions. We analyze the sample complexity of regret minimization in this repeated Stackelberg game. We show that depending on the reward structure, the existence of the omniscient follower may change the sample complexity drastically, from constant to exponential, even for linear cooperative Stackelberg games. This poses unique challenges for the learning process of the leader and the subsequent regret analysis.

Budget management strategies in repeated auctions have received growing attention in online advertising markets. However, previous work on budget management in online bidding mainly focused on second-price auctions. The rapid shift from second-price auctions to first-price auctions for online ads in recent years has motivated the challenging question of how to bid in repeated first-price auctions while controlling budgets. In this work, we study the problem of learning in repeated first-price auctions with budgets. We design a dual-based algorithm that can achieve a near-optimal $\widetilde{O}(\sqrt{T})$ regret with full information feedback where the maximum competing bid is always revealed after each auction. We further consider the setting with one-sided information feedback where only the winning bid is revealed after each auction. We show that our modified algorithm can still achieve an $\widetilde{O}(\sqrt{T})$ regret with mild assumptions on the bidder's value distribution. Finally, we complement the theoretical results with numerical experiments to confirm the effectiveness of our budget management policy.

Many problems, such as online ad display, can be formulated as online bipartite matching. The crucial challenge lies in the nature of sequentially-revealed online item information, based on which we make irreversible matching decisions at each step. While numerous expert online algorithms have been proposed with bounded worst-case competitive ratios, they may not offer satisfactory performance in average cases. On the other hand, reinforcement learning (RL) has been applied to improve the average performance, but it lacks robustness and can perform arbitrarily poorly. In this paper, we propose a novel RL-based approach to edge-weighted online bipartite matching with robustness guarantees (LOMAR), achieving both good average-case and worst-case performance. The key novelty of LOMAR is a new online switching operation which, based on a judicious condition to hedge against future uncertainties, decides whether to follow the expert's decision or the RL decision for each online item. We prove that for any $\rho\in[0,1]$, LOMAR is $\rho$-competitive against any given expert online algorithm. To improve the average performance, we train the RL policy by explicitly considering the online switching operation. Finally, we run empirical experiments to demonstrate the advantages of LOMAR compared to existing baselines.

Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex objectives on these domains, utilizing the principles of Sinkhorn matrix scaling and mirror descent. The proposed algorithm is robust to noise, and can be used in an online setting. We provide theoretical guarantees for convex objectives and experimental results showcasing it effectiveness on both synthetic and real-world data.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of $\ell$ predictors, we obtain a competitive ratio of $O(\ell^2)$, and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a $(1+\epsilon)$-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the $k$-server problem.

This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable. We propose a computational framework to approximate these $h$-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, and if the state dimension is large.

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta,\epsilon)$-stationary point from $O(\epsilon^{-4}\delta^{-1})$ stochastic gradient queries to $O(\epsilon^{-3}\delta^{-1})$, which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to *online learning*, after which our results follow from standard regret bounds in online learning. For *deterministic and second-order smooth* objectives, applying more advanced optimistic online learning techniques enables a new complexity of $O(\epsilon^{-1.5}\delta^{-0.5})$. Our improved non-smooth analysis also immediately recovers all optimal or best-known results for finding $\epsilon$ stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

We consider online learning in multi-player smooth monotone games. Existing algorithms have limitations such as (1) being only applicable to strongly monotone games; (2) lacking the no-regret guarantee; (3) having only asymptotic or slow $\mathcal{O}(\frac{1}{\sqrt{T}})$ last-iterate convergence rate to a Nash equilibrium. While the $\mathcal{O}(\frac{1}{\sqrt{T}})$ rate is tight for a large class of algorithms including the well-studied extragradient algorithm and optimistic gradient algorithm, it is not optimal for all gradient-based algorithms. We propose the *accelerated optimistic gradient* (AOG) algorithm, the first doubly optimal no-regret learning algorithm for smooth monotone games. Namely, our algorithm achieves both (i) the optimal $\mathcal{O}(\sqrt{T})$ regret in the adversarial setting under smooth and convex loss functions and (ii) the optimal $\mathcal{O}(\frac{1}{T})$ last-iterate convergence rate to a Nash equilibrium in multi-player smooth monotone games. As a byproduct of the accelerated last-iterate convergence rate, we further show that each player suffers only an $\mathcal{O}(\log T)$ individual *worst-case dynamic regret*, providing an exponential improvement over the previous state-of-the-art $\mathcal{O}(\sqrt{T})$ bound.

We consider an online learning problem with one-sided feedback, in which the learner is able to observe the true label only for positively predicted instances. On each round, $k$ instances arrive and receive classification outcomes according to a randomized policy deployed by the learner, whose goal is to maximize accuracy while deploying individually fair policies. We first present a novel auditing scheme, capable of utilizing feedback from dynamically-selected panels of multiple, possibly inconsistent, auditors regarding fairness violations. In particular, we show how our proposed auditing scheme allows for algorithmically exploring the resulting accuracy-fairness frontier, with no need for additional feedback from auditors. We then present an efficient reduction from our problem of online learning with one-sided feedback and a panel reporting fairness violations to the contextual combinatorial semi-bandit problem (Cesa-Bianchi & Lugosi, 2009; Gyorgy et al., 2007), allowing us to leverage algorithms for contextual combinatorial semi-bandits to establish multi-criteria no regret guarantees in our setting, simultaneously for accuracy and fairness. Our results eliminate two potential sources of bias from prior work: the “hidden outcomes” that are not available to an algorithm operating in the full information setting, and human biases that might be present in any single human auditor, but can be mitigated by selecting a well-chosen panel.

This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a variable-duplication technique that copies each variable $K$ times and reduces the optimality gap and constraint violation by a factor of $\sqrt{K}$. Furthermore, we show how online algorithms can be effectively integrated into sifting, a column generation scheme for large-scale LPs. Numerical experiments demonstrate that our methods can serve as either an approximate direct solver, or an initialization subroutine for exact LP solving.

Federated machine unlearning (FMU) aims to remove the influence of a specified subset of training data upon request from a trained federated learning model. Despite achieving remarkable performance, existing FMU techniques suffer from inefficiency due to two sequential operations of training and retraining/unlearning on large-scale datasets. Our prior study, PCMU, was proposed to improve the efficiency of centralized machine unlearning (CMU) with certified guarantees, by simultaneously executing the training and unlearning operations. This paper proposes a fast FMU algorithm, FFMU, for improving the FMU efficiency while maintaining the unlearning quality. The PCMU method is leveraged to train a local machine learning (MU) model on each edge device. We propose to employ nonlinear functional analysis techniques to refine the local MU models as output functions of a Nemytskii operator. We conduct theoretical analysis to derive that the Nemytskii operator has a global Lipschitz constant, which allows us to bound the difference between two MU models regarding the distance between their gradients. Based on the Nemytskii operator and average smooth local gradients, the global MU model on the server is guaranteed to achieve close performance to each local MU model with the certified guarantees.

We study the online restless bandit problem, where each arm evolves according to a Markov chain independently, and the reward of pulling an arm depends on both the current state of the corresponding Markov chain and the pulled arm. The agent (decision maker) does not know the transition functions and reward functions, and cannot observe the states of arms even after pulling. The goal is to sequentially choose which arms to pull so as to maximize the expected cumulative rewards collected. In this paper, we propose TSEETC, a learning algorithm based on Thompson Sampling with Episodic Explore-Then-Commit. The algorithm proceeds in episodes of increasing length and each episode is divided into exploration and exploitation phases. During the exploration phase, samples of action-reward pairs are collected in a round-robin fashion and utilized to update the posterior distribution as a mixture of Dirichlet distributions. At the beginning of the exploitation phase, TSEETC generates a sample from the posterior distribution as true parameters. It then follows the optimal policy for the sampled model for the rest of the episode. We establish the Bayesian regret bound $\tilde {\mathcal{O}}(\sqrt{T})$ for TSEETC, where $T$ is the time horizon. We show through simulations that TSEETC outperforms existing algorithms in regret.

We consider online scheduling on unrelated (heterogeneous) machines in a speed-oblivious setting, where an algorithm is unaware of the exact job-dependent processing speeds. We show strong impossibility results for clairvoyant and non-clairvoyant algorithms and overcome them in models inspired by practical settings: (i) we provide competitive learning-augmented algorithms, assuming that (possibly erroneous) predictions on the speeds are given, and (ii) we provide competitive algorithms for the speed-ordered model, where a single global order of machines according to their unknown job-dependent speeds is known. We prove strong theoretical guarantees and evaluate our findings on a representative heterogeneous multi-core processor. These seem to be the first empirical results for scheduling algorithms with predictions that are evaluated in a non-synthetic hardware environment.

In recent years, online search has been playing an increasingly important role in imperfect information games (IIGs). Previous online search is known as common-knowledge subgame solving, which has to consider all the states in a common-knowledge closure. This is only computationally tolerable for medium size games, such as poker. To handle larger games, order-1 Knowledge-Limited Subgame Solving (1-KLSS) only considers the states in a knowledge-limited closure, which results in a much smaller subgame. However, 1-KLSS is unsafe. In this paper, we first extend 1-KLSS to Safe-1-KLSS and prove its safeness. To make Safe-1-KLSS applicable to even larger games, we propose Opponent-Limited Subgame Solving (OLSS) to limit how the opponent reaches a subgame and how it acts in the subgame. Limiting the opponent's strategy dramatically reduces the subgame size and improves the efficiency of subgame solving while still preserving some safety in the limit. Experiments in medium size poker show that Safe-1-KLSS and OLSS are orders of magnitude faster than previous common-knowledge subgame solving. Also, OLSS significantly improves the online performance in a two-player Mahjong game, whose game size prohibits the use of previous common-knowledge subgame-solving methods.

We present the OMG-CMDP! algorithm for regret minimization in adversarial Contextual MDPs. The algorithm operates under the minimal assumptions of realizable function class and access to online least squares and log loss regression oracles. Our algorithm is efficient (assuming efficient online regression oracles), simple and robust to approximation errors. It enjoys an $\widetilde{O}(H^{2.5} \sqrt{ T|S||A| ( \mathcal{R}\_{TH}(\mathcal{O}) + H \log(\delta^{-1}) )})$ regret guarantee, with $T$ being the number of episodes, $S$ the state space, $A$ the action space, $H$ the horizon and $\mathcal{R}\_{TH}(\mathcal{O}) = \mathcal{R}\_{TH}(\mathcal{O}\_{sq}^\mathcal{F}) + \mathcal{R}\_{TH}(\mathcal{O}\_{log}^\mathcal{P})$ is the sum of the square and log-loss regression oracles' regret, used to approximate the context-dependent rewards and dynamics, respectively. To the best of our knowledge, our algorithm is the first efficient rate optimal regret minimization algorithm for adversarial CMDPs that operates under the minimal standard assumption of online function approximation.

Algorithms for online learning typically require one or more boundedness assumptions: that the domain is bounded, that the losses are Lipschitz, or both. In this paper, we develop a new setting for online learning with unbounded domains and non-Lipschitz losses. For this setting we provide an algorithm which guarantees $R_{T}(u)\le \tilde O(G\|u\|\sqrt{T}+L\|u\|^{2}\sqrt{T})$ regret on any problem where the subgradients satisfy $\|g_{t}\|\le G+L\|w_{t}\|$, and show that this bound is unimprovable without further assumptions. We leverage this algorithm to develop new saddle-point optimization algorithms that converge in duality gap in unbounded domains, even in the absence of meaningful curvature. Finally, we provide the first algorithm achieving non-trivial dynamic regret in an unbounded domain for non-Lipschitz losses, as well as a matching lower bound. The regret of our dynamic regret algorithm automatically improves to a novel $L^{*}$ bound when the losses are smooth.

In this paper, we introduce a variant of Bayesian online change point detection with a reducedrank Student-t process (TP) and dependent Student-t noise, as a nonparametric time series model. Our method builds and improves upon the state-of-the-art Gaussian process (GP) change point model benchmark of Saatci et al. (2010). The Student-t process generalizes the concept of a GP and hence yields a more flexible alternative. Additionally, unlike a GP, the predictive variance explicitly depends on the training observations, while the use of an entangled Student-t noise model preserves analytical tractability. Our approach also uses a Hilbert space reduced-rank representation of the TP kernel, derived from an eigenfunction expansion of the Laplace operator (Solin & Sarkka, 2020), to alleviate its computational complexity. Improvements in prediction and training time are demonstrated with real-world data-sets

Many real-world multi-label prediction problems involve set-valued predictions that must satisfy specific requirements dictated by downstream usage. We focus on a typical scenario where such requirements, separately encoding *value* and *cost*, compete with each other. For instance, a hospital might expect a smart diagnosis system to capture as many severe, often co-morbid, diseases as possible (the value), while maintaining strict control over incorrect predictions (the cost). We present a general pipeline, dubbed as FavMac, to maximize the value while controlling the cost in such scenarios. FavMac can be combined with almost any multi-label classifier, affording distribution-free theoretical guarantees on cost control. Moreover, unlike prior works, FavMac can handle real-world large-scale applications via a carefully designed online update mechanism, which is of independent interest. Our methodological and theoretical contributions are supported by experiments on several healthcare tasks and synthetic datasets - FavMac furnishes higher value compared with several variants and baselines while maintaining strict cost control.