ICML 2022 Papers

Motivated by many applications, we study clustering with a faulty oracle. In this problem, there are $n$ items belonging to $k$ unknown clusters, and the algorithm is allowed to ask the oracle whether two items belong to the same cluster or not. However, the answer from the oracle is correct only with probability $\frac{1}{2}+\frac{\delta}{2}$. The goal is to recover the hidden clusters with minimum number of noisy queries. Previous works have shown that the problem can be solved with $O(\frac{nk\log n}{\delta^2} + \text{poly}(k,\frac{1}{\delta}, \log n))$ queries, while $\Omega(\frac{nk}{\delta^2})$ queries is known to be necessary. So, for any values of $k$ and $\delta$, there is still a non-trivial gap between upper and lower bounds. In this work, we obtain the first matching upper and lower bounds for a wide range of parameters. In particular, a new polynomial time algorithm with $O(\frac{n(k+\log n)}{\delta^2} + \text{poly}(k,\frac{1}{\delta}, \log n))$ queries is proposed. Moreover, we prove a new lower bound of $\Omega(\frac{n\log n}{\delta^2})$, which, combined with the existing $\Omega(\frac{nk}{\delta^2})$ bound, matches our upper bound up to an additive $\text{poly}(k,\frac{1}{\delta},\log n)$ term. To obtain the new results, our main ingredient is an interesting connection between our problem and multi-armed bandit, which might provide useful insights for other similar problems.

Data clipping is crucial in reducing noise in quantization operations and improving the achievable accuracy of quantization-aware training (QAT). Current practices rely on heuristics to set clipping threshold scalars and cannot be shown to be optimal. We propose Optimally Clipped Tensors And Vectors (OCTAV), a recursive algorithm to determine MSE-optimal clipping scalars. Derived from the fast Newton-Raphson method, OCTAV finds optimal clipping scalars on the fly, for every tensor, at every iteration of the QAT routine. Thus, the QAT algorithm is formulated with provably minimum quantization noise at each step. In addition, we reveal limitations in common gradient estimation techniques in QAT and propose magnitude-aware differentiation as a remedy to further improve accuracy. Experimentally, OCTAV-enabled QAT achieves state-of-the-art accuracy on multiple tasks. These include training-from-scratch and retraining ResNets and MobileNets on ImageNet, and Squad fine-tuning using BERT models, where OCTAV-enabled QAT consistently preserves accuracy at low precision (4-to-6-bits). Our results require no modifications to the baseline training recipe, except for the insertion of quantization operations where appropriate.

In this paper, we investigate the problem of stochastic multi-level compositional optimization, where the objective function is a composition of multiple smooth but possibly non-convex functions. Existing methods for solving this problem either suffer from sub-optimal sample complexities or need a huge batch size. To address this limitation, we propose a Stochastic Multi-level Variance Reduction method (SMVR), which achieves the optimal sample complexity of $\mathcal{O}\left(1 / \epsilon^{3}\right)$ to find an $\epsilon$-stationary point for non-convex objectives. Furthermore, when the objective function satisfies the convexity or Polyak-{Ł}ojasiewicz (PL) condition, we propose a stage-wise variant of SMVR and improve the sample complexity to $\mathcal{O}\left(1 / \epsilon^{2}\right)$ for convex functions or $\mathcal{O}\left(1 /(\mu\epsilon)\right)$ for non-convex functions satisfying the $\mu$-PL condition. The latter result implies the same complexity for $\mu$-strongly convex functions. To make use of adaptive learning rates, we also develop Adaptive SMVR, which achieves the same optimal complexities but converges faster in practice. All our complexities match the lower bounds not only in terms of $\epsilon$ but also in terms of $\mu$ (for PL or strongly convex functions), without using a large batch size in each iteration.

We study the problem of mean estimation of $\ell_2$-bounded vectors under the constraint of local differential privacy. While the literature has a variety of algorithms that achieve the (asymptotic) optimal rates for this problem, the performance of these algorithms in practice can vary significantly due to varying (and often large) hidden constants. In this work, we investigate the question of designing the randomizer with the smallest variance. We show that PrivUnit (Bhowmick et al. 2018) with optimized parameters achieves the optimal variance among a large family of natural randomizers. To prove this result, we establish some properties of local randomizers, and use symmetrization arguments that allow us to write the optimal randomizer as the optimizer of a certain linear program. These structural results, which should extend to other problems, then allow us to show that the optimal randomizer belongs to the PrivUnit family. We also develop a new variant of PrivUnit based on the Gaussian distribution which is more amenable to mathematical analysis and enjoys the same optimality guarantees. This allows us to establish several useful properties on the exact constants of the optimal error as well as to numerically estimate these constants.

Deep neural networks usually perform poorly when the training dataset suffers from extreme class imbalance. Recent studies found that directly training with out-of-distribution data (i.e., open-set samples) in a semi-supervised manner would harm the generalization performance. In this work, we theoretically show that out-of-distribution data can still be leveraged to augment the minority classes from a Bayesian perspective. Based on this motivation, we propose a novel method called Open-sampling, which utilizes open-set noisy labels to re-balance the class priors of the training dataset. For each open-set instance, the label is sampled from our pre-defined distribution that is complementary to the distribution of original class priors. We empirically show that Open-sampling not only re-balances the class priors but also encourages the neural network to learn separable representations. Extensive experiments demonstrate that our proposed method significantly outperforms existing data re-balancing methods and can boost the performance of existing state-of-the-art methods.

The recently developed average-case analysis of optimization methods allows a more fine-grained and representative convergence analysis than usual worst-case results. In exchange, this analysis requires a more precise hypothesis over the data generating process, namely assuming knowledge of the expected spectral distribution (ESD) of the random matrix associated with the problem. This work shows that the concentration of eigenvalues near the edges of the ESD determines a problem’s asymptotic average complexity. This a priori information on this concentration is a more grounded assumption than complete knowledge of the ESD. This approximate concentration is effectively a middle ground between the coarseness of the worst-case scenario convergence and the restrictive previous average-case analysis. We also introduce the Generalized Chebyshev method, asymptotically optimal under a hypothesis on this concentration and globally optimal when the ESD follows a Beta distribution. We compare its performance to classical optimization algorithms, such as gradient descent or Nesterov’s scheme, and we show that, in the average-case context, Nesterov’s method is universally nearly optimal asymptotically.

In the correlation clustering problem the input is a signed graph where the sign indicates whether each pair of points should be placed in the same cluster or not. The goal of the problem is to compute a clustering which minimizes the number of disagreements with such recommendation. Thanks to its many practical applications, correlation clustering is a fundamental unsupervised learning problem and has been extensively studied in many different settings. In this paper we study the problem in the classic online setting with recourse; The vertices of the graphs arrive in an online manner and the goal is to maintain an approximate clustering while minimizing the number of times each vertex changes cluster. Our main contribution is an algorithm that achieves logarithmic recourse per vertex in the worst case. We also complement this result with a tight lower bound. Finally we show experimentally that our algorithm achieves better performances than state-of-the-art algorithms on real world data.

Motivated by applications to online learning in sparse estimation and Bayesian optimization, we consider the problem of online unconstrained nonsubmodular minimization with delayed costs in both full information and bandit feedback settings. In contrast to previous works on online unconstrained submodular minimization, we focus on a class of nonsubmodular functions with special structure, and prove regret guarantees for several variants of the online and approximate online bandit gradient descent algorithms in static and delayed scenarios. We derive bounds for the agent’s regret in the full information and bandit feedback setting, even if the delay between choosing a decision and receiving the incurred cost is unbounded. Key to our approach is the notion of $(\alpha, \beta)$-regret and the extension of the generic convex relaxation model from \citet{El-2020-Optimal}, the analysis of which is of independent interest. We conduct and showcase several simulation studies to demonstrate the efficacy of our algorithms.

We study online learning problems in which a decision maker wants to maximize their expected reward without violating a finite set of $m$ resource constraints. By casting the learning process over a suitably defined space of strategy mixtures, we recover strong duality on a Lagrangian relaxation of the underlying optimization problem, even for general settings with non-convex reward and resource-consumption functions. Then, we provide the first best-of-both-worlds type framework for this setting, with no-regret guarantees both under stochastic and adversarial inputs. Our framework yields the same regret guarantees of prior work in the stochastic case. On the other hand, when budgets grow at least linearly in the time horizon, it allows us to provide a constant competitive ratio in the adversarial case, which improves over the $O(m \log T)$ competitive ratio of Immorlica et al. [FOCS’19]. Moreover, our framework allows the decision maker to handle non-convex reward and cost functions. We provide two game-theoretic applications of our framework to give further evidence of its flexibility.

Two central problems in Stochastic Optimization are Min-Sum Set Cover and Pandora’s Box. In Pandora’s Box, we are presented with n boxes, each containing an unknown value and the goal is to open the boxes in some order to minimize the sum of the search cost and the smallest value found. Given a distribution of value vectors, we are asked to identify a near-optimal search order. Min-Sum Set Cover corresponds to the case where values are either 0 or infinity. In this work, we study the case where the value vectors are not drawn from a distribution but are presented to a learner in an online fashion. We present a computationally efficient algorithm that is constant-competitive against the cost of the optimal search order. We extend our results to a bandit setting where only the values of the boxes opened are revealed to the learner after every round. We also generalize our results to other commonly studied variants of Pandora’s Box and Min-Sum Set Cover that involve selecting more than a single value subject to a matroid constraint.

We consider a price-based revenue management problem with reusable resources over a finite time horizon $T$. The problem finds important applications in car/bicycle rental, ridesharing, cloud computing, and hospitality management. Customers arrive following a price-dependent Poisson process and each customer requests one unit of $c$ homogeneous reusable resources. If there is an available unit, the customer gets served within a price-dependent exponentially distributed service time; otherwise, she waits in a queue until the next available unit. The decision maker assumes that the inter-arrival and service intervals have an unknown linear dependence on a $d_f$-dimensional feature vector associated with the posted price. We propose a rate-optimal online learning and pricing algorithm, termed Batch Linear Confidence Bound (BLinUCB), and prove that the cumulative regret is $\tilde{O}( d_f \sqrt{T } )$. In establishing the regret, we bound the transient system performance upon price changes via a coupling argument, and also generalize linear bandits to accommodate sub-exponential rewards.

Recent work has shown that offline reinforcement learning (RL) can be formulated as a sequence modeling problem (Chen et al., 2021; Janner et al., 2021) and solved via approaches similar to large-scale language modeling. However, any practical instantiation of RL also involves an online component, where policies pretrained on passive offline datasets are finetuned via task-specific interactions with the environment. We propose Online Decision Transformers (ODT), an RL algorithm based on sequence modeling that blends offline pretraining with online finetuning in a unified framework. Our framework uses sequence-level entropy regularizers in conjunction with autoregressive modeling objectives for sample-efficient exploration and finetuning. Empirically, we show that ODT is competitive with the state-of-the-art in absolute performance on the D4RL benchmark but shows much more significant gains during the finetuning procedure.

This paper proposed a new online continual learning approach called OCM based on

We consider the experimental design problem in an online environment, an important practical task for reducing the variance of estimates in randomized experiments which allows for greater precision, and in turn, improved decision making. In this work, we present algorithms that build on recent advances in online discrepancy minimization which accommodate both arbitrary treatment probabilities and multiple treatments. The proposed algorithms are computational efficient, minimize covariate imbalance, and include randomization which enables robustness to misspecification. We provide worst case bounds on the expected mean squared error of the causal estimate and show that the proposed estimator is no worse than an implicit ridge regression, which are within a logarithmic factor of the best known results for offline experimental design. We conclude with a detailed simulation study showing favorable results relative to complete randomization as well as to offline methods for experimental design with time complexities exceeding our algorithm, which has a linear dependence on the number of observations, by polynomial factors.

This paper studies online algorithms augmented with

Active regression considers a linear regression problem where the learner receives a large number of data points but can only observe a small number of labels. Since online algorithms can deal with incremental training data and take advantage of low computational cost, we consider an online extension of the active regression problem: the learner receives data points one by one and immediately decides whether it should collect the corresponding labels. The goal is to efficiently maintain the regression of received data points with a small budget of label queries. We propose novel algorithms for this problem under $\ell_p$ loss where $p\in[1,2]$. To achieve a $(1+\epsilon)$-approximate solution, our proposed algorithms only requires $\tilde{\mathcal{O}}(d/poly(\epsilon))$ queries of labels. The numerical results verify our theoretical results and show that our methods have comparable performance with offline active regression algorithms.

A popular approach to reduce the size of a massive dataset is to apply efficient online sampling to the stream of data as it is read or generated. Online sampling routines are currently restricted to variations of reservoir sampling, where each sample is selected uniformly and independently of other samples. This renders them unsuitable for large-scale applications in computational biology, such as metagenomic community profiling and protein function annotation, which suffer from severe class imbalance. To maintain a representative and diverse sample, we must identify and preferentially select data that are likely to belong to rare classes. We argue that existing schemes for diversity sampling have prohibitive overhead for large-scale problems and high-throughput streams. We propose an efficient sampling routine that uses an online representation of the data distribution as a prefilter to retain elements from rare groups. We apply this method to several genomic data analysis tasks and demonstrate significant speedup in downstream analysis without sacrificing the quality of the results. Because our algorithm is 2x faster and uses 1000x less memory than coreset, reservoir and sketch-based alternatives, we anticipate that it will become a useful preprocessing step for applications with large-scale streaming data.

In this paper, we initiate the study of one-pass algorithms for solving the maximum-a-posteriori (MAP) inference problem for Non-symmetric Determinantal Point Processes (NDPPs). In particular, we formulate streaming and online versions of the problem and provide one-pass algorithms for solving these problems. In our streaming setting, data points arrive in an arbitrary order and the algorithms are constrained to use a single-pass over the data as well as sub-linear memory, and only need to output a valid solution at the end of the stream. Our online setting has an additional requirement of maintaining a valid solution at any point in time. We design new one-pass algorithms for these problems and show that they perform comparably to (or even better than) the offline greedy algorithm while using substantially lower memory.

Contrastive representation learning encourages data representation to make semantically similar pairs closer than randomly drawn negative samples, which has been successful in various domains such as vision, language, and graphs. Recent theoretical studies have attempted to explain the benefit of the large negative sample size by upper-bounding the downstream classification loss with the contrastive loss. However, the previous surrogate bounds have two drawbacks: they are only legitimate for a limited range of negative sample sizes and prohibitively large even within that range. Due to these drawbacks, there still does not exist a consensus on how negative sample size theoretically correlates with downstream classification performance. Following the simplified setting where positive pairs are drawn from the true distribution (not generated by data augmentation; as supposed in previous studies), this study establishes surrogate upper and lower bounds for the downstream classification loss for all negative sample sizes that best explain the empirical observations on the negative sample size in the earlier studies. Our bounds suggest that the contrastive loss can be viewed as a surrogate objective of the downstream loss and larger negative sample sizes improve downstream classification because the surrogate gap between contrastive and supervised losses decays. We verify that our theory is consistent with experiments on synthetic, vision, and language datasets.