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The K-armed dueling bandit problem, where the feedback is in the form of noisy pairwise comparisons, has been widely studied. Previous works have only focused on the sequential setting where the policy adapts after every comparison. However, in many applications such as search ranking and recommendation systems, it is preferable to perform comparisons in a limited number of parallel batches. We study the batched K-armed dueling bandit problem under two standard settings: (i) existence of a Condorcet winner, and (ii) strong stochastic transitivity and stochastic triangle inequality. For both settings, we obtain algorithms with a smooth trade-off between the number of batches and regret. Our regret bounds match the best known sequential regret bounds (up to poly-logarithmic factors), using only a logarithmic number of batches. We complement our regret analysis with a nearly-matching lower bound. Finally, we also validate our theoretical results via experiments on synthetic and real data.

We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. 2012 for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order $\widetilde{\mathcal{O}}(\sqrt{H^3SAT})$ where $H$ is the length of one episode, $S$ is the number of states, $A$ the number of actions, $T$ the number of episodes, that matches the lower-bound of $\Omega(\sqrt{H^3SAT})$ up to poly-$\log$ terms in $H,S,A,T$ for a large enough $T$. To the best of our knowledge, this is the first algorithm that obtains an optimal dependence on the horizon $H$ (and $S$) \textit{without the need of an involved Bernstein-like bonus or noise.} Crucial to our analysis is a new fine-grained anti-concentration bound for a weighted Dirichlet sum that can be of independent interest. We then explain how Bayes-UCBVI can be easily extended beyond the tabular setting, exhibiting a strong link between our algorithm and Bayesian bootstrap (Rubin,1981).

Compositional generalization is a critical ability in learning and decision-making. We focus on the setting of reinforcement learning in object-oriented environments to study compositional generalization in world modeling. We (1) formalize the compositional generalization problem with an algebraic approach and (2) study how a world model can achieve that. We introduce a conceptual environment, Object Library, and two instances, and deploy a principled pipeline to measure the generalization ability. Motivated by the formulation, we analyze several methods with exact or no compositional generalization ability using our framework, and design a differentiable approach, Homomorphic Object-oriented World Model (HOWM), that achieves soft but more efficient compositional generalization.

Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high dimensional data. Many of them rely on a non-parametric nearest neighbours approach which suffers from the curse of dimensionality. We attempt to address that challenge by proposing a novel approach to the problem: Local Intrinsic Dimension estimation using approximate Likelihood (LIDL).Our method relies on an arbitrary density estimation method as its subroutine, and hence tries to sidestep the dimensionality challenge by making use of the recent progress in parametric neural methods for likelihood estimation.We carefully investigate the empirical properties of the proposed method, compare them with our theoretical predictions, show that LIDL yields competitive results on the standard benchmarks for this problem, and that it scales to thousands of dimensions. What is more, we anticipate this approach to improve further with the continuing advances in the density estimation literature.

Universal methods achieve optimal convergence rate guarantees in convex optimization without any prior knowledge of the problem's regularity parameters or the attributes of the gradient oracle employed by the method. In this regard, existing state-of-the-art algorithms achieve an $O(1/T^2)$ convergence rate in Lipschitz smooth problems with a perfect gradient oracle, and an $O(1/sqrt{T})$ convergence speed when the underlying problem is non-smooth and/or the gradient oracle is stochastic. On the downside, these methods do not take into account the dependence of these guarantees on the problem's dimensionality, and this can have a catastrophic impact on a method's convergence, in both theory and practice. Our paper aims to bridge this gap by providing a scalable universal method - dubbed UnDERGrad - which enjoys an almost dimension-free oracle complexity in problems with a favorable geometry (like the simplex, $\ell_1$-ball or trace-constraints), while retaining the order-optimal dependence on T described above. These "best of both worlds" guarantees are achieved via a primal-dual update scheme inspired by the dual exploration method for variational inequalities.

Large neural networks excel in many domains, but they are expensive to train and fine-tune. A popular approach to reduce their compute or memory requirements is to replace dense weight matrices with structured ones (e.g., sparse, low-rank, Fourier transform). These methods have not seen widespread adoption (1) in end-to-end training due to unfavorable efficiency--quality tradeoffs, and (2) in dense-to-sparse fine-tuning due to lack of tractable algorithms to approximate a given dense weight matrix. To address these issues, we propose a class of matrices (Monarch) that is hardware-efficient (they are parameterized as products of two block-diagonal matrices for better hardware utilization) and expressive (they can represent many commonly used transforms). Surprisingly, the problem of approximating a dense weight matrix with a Monarch matrix, though nonconvex, has an analytical optimal solution. These properties of Monarch matrices unlock new ways to train and fine-tune sparse and dense models. We empirically validate that Monarch can achieve favorable accuracy-efficiency tradeoffs in several end-to-end sparse training applications: speeding up ViT and GPT-2 training on ImageNet classification and Wikitext-103 language modeling by 2x with comparable model quality, and reducing the error on PDE solving and MRI reconstruction tasks by 40%. In sparse-to-dense training, with a simple technique called "reverse sparsification," Monarch matrices serve as a useful intermediate representation to speed up GPT-2 pretraining on OpenWebText by 2x without quality drop. The same technique brings 23% faster BERT pretraining than even the very optimized implementation from Nvidia that set the MLPerf 1.1 record. In dense-to-sparse fine-tuning, as a proof-of-concept, our Monarch approximation algorithm speeds up BERT fine-tuning on GLUE by 1.7x with comparable accuracy.

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.

Learning meaningful representations of data that can address challenges such as batch effect correction and counterfactual inference is a central problem in many domains including computational biology. Adopting a Conditional VAE framework, we show that marginal independence between the representation and a condition variable plays a key role in both of these challenges. We propose the Contrastive Mixture of Posteriors (CoMP) method that uses a novel misalignment penalty defined in terms of mixtures of the variational posteriors to enforce this independence in latent space. We show that CoMP has attractive theoretical properties compared to previous approaches, and we prove counterfactual identifiability of CoMP under additional assumptions. We demonstrate state-of-the-art performance on a set of challenging tasks including aligning human tumour samples with cancer cell-lines, predicting transcriptome-level perturbation responses, and batch correction on single-cell RNA sequencing data. We also find parallels to fair representation learning and demonstrate that CoMP is competitive on a common task in the field.

We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPGs). To learn a Nash equilibrium of an MPG in which the size of state space and/or the number of players can be very large, we propose new independent policy gradient algorithms that are run by all players in tandem. When there is no uncertainty in the gradient evaluation, we show that our algorithm finds an $\epsilon$-Nash equilibrium with $O(1/\epsilon^2)$ iteration complexity which does not explicitly depend on the state space size. When the exact gradient is not available, we establish $O(1/\epsilon^5)$ sample complexity bound in a potentially infinitely large state space for a sample-based algorithm that utilizes function approximation. Moreover, we identify a class of independent policy gradient algorithms that enjoy convergence for both zero-sum Markov games and Markov cooperative games with the players that are oblivious to the types of games being played. Finally, we provide computational experiments to corroborate the merits and the effectiveness of our theoretical developments.

A major challenge in studying robustness in deep learning is defining the set of ``meaningless'' perturbations to which a given Neural Network (NN) should be invariant. Most work on robustness implicitly uses a human as the reference model to define such perturbations. Our work offers a new view on robustness by using another reference NN to define the set of perturbations a given NN should be invariant to, thus generalizing the reliance on a reference ``human NN'' to any NN. This makes measuring robustness equivalent to measuring the extent to which two NNs share invariances.We propose a measure called \stir, which faithfully captures the extent to which two NNs share invariances. \stir re-purposes existing representation similarity measures to make them suitable for measuring shared invariances. Using our measure, we are able to gain insights about how shared invariances vary with changes in weight initialization, architecture, loss functions, and training dataset. Our implementation is available at: \url{https://github.com/nvedant07/STIR}.

We consider unsupervised domain adaptation (UDA), where labeled data from a source domain (e.g., photos) and unlabeled data from a target domain (e.g., sketches) are used to learn a classifier for the target domain. Conventional UDA methods (e.g., domain adversarial training) learn domain-invariant features to generalize from the source domain to the target domain. In this paper, we show that contrastive pre-training, which learns features on unlabeled source and target data and then fine-tunes on labeled source data, is competitive with strong UDA methods. However, we find that contrastive pre-training does not learn domain-invariant features, diverging from conventional UDA intuitions. We show theoretically that contrastive pre-training can learn features that vary subtantially across domains but still generalize to the target domain, by disentangling domain and class information. We empirically validate our theory on benchmark vision datasets.

A popular paradigm in robotic learning is to train a policy from scratch for every new robot. This is not only inefficient but also often impractical for complex robots. In this work, we consider the problem of transferring a policy across two different robots with significantly different parameters such as kinematics and morphology. Existing approaches that train a new policy by matching the action or state transition distribution, including imitation learning methods, fail due to optimal action and/or state distribution being mismatched in different robots. In this paper, we propose a novel method named REvolveR of using continuous evolutionary models for robotic policy transfer implemented in a physics simulator. We interpolate between the source robot and the target robot by finding a continuous evolutionary change of robot parameters. An expert policy on the source robot is transferred through training on a sequence of intermediate robots that gradually evolve into the target robot. Experiments on a physics simulator show that the proposed continuous evolutionary model can effectively transfer the policy across robots and achieve superior sample efficiency on new robots. The proposed method is especially advantageous in sparse reward settings where exploration can be significantly reduced.

Model-based reinforcement learning methods often use learning only for the purpose of recovering an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers.While conceptually simple, this combination has a number of empirical shortcomings, suggesting that learned models may not be well-suited to standard trajectory optimization.In this paper, we consider what it would look like to fold as much of the trajectory optimization pipeline as possible into the modeling problem, such that sampling from the model and planning with it become nearly identical.The core of our technical approach lies in a diffusion probabilistic model that plans by iteratively denoising trajectories.We show how classifier-guided sampling and image inpainting can be reinterpreted as coherent planning strategies, explore the unusual and useful properties of diffusion-based planning methods, and demonstrate the effectiveness of our framework in control settings that emphasize long-horizon decision-making and test-time flexibility.

Recent investigations in noise contrastive estimation suggest, both empirically as well as theoretically, that while having more ``negative samples'' in the contrastive loss improves downstream classification performance initially, beyond a threshold, it hurts downstream performance due to a ``collision-coverage'' trade-off. But is such a phenomenon inherent in contrastive learning?We show in a simple theoretical setting, where positive pairs are generated by sampling from the underlying latent class (introduced by Saunshi et al. (ICML 2019)), that the downstream performance of the representation optimizing the (population) contrastive loss in fact does not degrade with the number of negative samples. Along the way, we give a structural characterization of the optimal representation in our framework, for noise contrastive estimation. We also provide empirical support for our theoretical results on CIFAR-10 and CIFAR-100 datasets.

In contrast to SGD, adaptive gradient methods like Adam allow robust training of modern deep networks, especially large language models. However, the use of adaptivity not only comes at the cost of extra memory but also raises the fundamental question: can non-adaptive methods like SGD enjoy similar benefits?In this paper, we provide an affirmative answer to this question by proposing to achieve both robust and memory-efficient training via the following general recipe: (1) modify the architecture and make it scale invariant, (2) train with SGD and weight decay, and optionally (3) clip the global gradient norm proportional to weight norm multiplied by $\sqrt{\frac{2\lambda}{\eta}}$, where $\eta$ is learning rate and $\lambda$ is weight decay. We show that this general approach is robust to rescaling of parameter and loss by proving that its convergence only depends logarithmically on the scale of initialization and loss, whereas the standard SGD might not even converge for many initializations. Following our recipe, we design a scale invariant version of BERT, called SIBERT, which when trained simply by vanilla SGD achieves performance comparable to BERT trained by adaptive methods like Adam on downstream tasks.

To prevent unintentional data leakage, research community has resorted to data generators that can produce differentially private data for model training. However, for the sake of the data privacy, existing solutions suffer from either expensive training cost or poor generalization performance. Therefore, we raise the question whether training efficiency and privacy can be achieved simultaneously. In this work, we for the first time identify that dataset condensation (DC) which is originally designed for improving training efficiency is also a better solution to replace the traditional data generators for private data generation, thus providing privacy for free. To demonstrate the privacy benefit of DC, we build a connection between DC and differential privacy, and theoretically prove on linear feature extractors (and then extended to non-linear feature extractors) that the existence of one sample has limited impact ($O(m/n)$) on the parameter distribution of networks trained on $m$ samples synthesized from $n (n \gg m)$ raw samples by DC. We also empirically validate the visual privacy and membership privacy of DC-synthesized data by launching both the loss-based and the state-of-the-art likelihood-based membership inference attacks. We envision this work as a milestone for data-efficient and privacy-preserving machine learning.

When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$, Conformal Prediction (CP) is a methodology that allows to estimate a confidence set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of the data is exchangeable. CP sets have guaranteed coverage for any finite population size $n$. While appealing, the computation of such a set turns out to be infeasible in general, \eg when the unknown variable $y_{n+1}$ is continuous. The bottleneck is that it is based on a procedure that readjusts a prediction model on data where we replace the unknown target by all its possible values in order to select the most probable one. This requires computing an infinite number of models, which often makes it intractable. In this paper, we combine CP techniques with classical algorithmic stability bounds to derive a prediction set computable with a single model fit. We demonstrate that our proposed confidence set does not lose any coverage guarantees while avoiding the need for data splitting as currently done in the literature. We provide some numerical experiments to illustrate the tightness of our estimation when the sample size is sufficiently large, on both synthetic and real datasets.

Spurious correlations pose a major challenge for robust machine learning. Models trained with empirical risk minimization (ERM) may learn to rely on correlations between class labels and spurious attributes, leading to poor performance on data groups without these correlations. This is challenging to address when the spurious attribute labels are unavailable. To improve worst-group performance on spuriously correlated data without training attribute labels, we propose Correct-N-Contrast (CNC), a contrastive approach to directly learn representations robust to spurious correlations. As ERM models can be good spurious attribute predictors, CNC works by (1) using a trained ERM model’s outputs to identify samples with the same class but dissimilar spurious features, and (2) training a robust model with contrastive learning to learn similar representations for these samples. To support CNC, we introduce new connections between worst-group error and a representation alignment loss that CNC aims to minimize. We empirically observe that worst-group error closely tracks with alignment loss, and prove that the alignment loss over a class helps upper-bound the class's worst-group vs. average error gap. On popular benchmarks, CNC reduces alignment loss drastically, and achieves state-of-the-art worst-group accuracy by 3.6% average absolute lift. CNC is also competitive with oracle methods that require group labels.

We study a variant of a recently introduced min-max optimization framework where the max-player is constrained to update its parameters in a greedy manner until it reaches a first-order stationary point. Our equilibrium definition for this framework depends on a proposal distribution which the min-player uses to choose directions in which to update its parameters. We show that, given a smooth and bounded nonconvex-nonconcave objective function, access to any proposal distribution for the min-player’s updates, and stochastic gradient oracle for the max-player, our algorithm converges to the aforementioned approximate local equilibrium in a number of iterations that does not depend on the dimension. The equilibrium point found by our algorithm depends on the proposal distribution, and when applying our algorithm to train GANs we choose the proposal distribution to be a distribution of stochastic gradients. We empirically evaluate our algorithm on challenging nonconvex-nonconcave test-functions and loss functions arising in GAN training. Our algorithm converges on these test functions and, when used to train GANs, trains stably on synthetic and real-world datasets and avoids mode collapse.

Bayesian structure learning allows one to capture uncertainty over the causal directed acyclic graph (DAG) responsible for generating given data. In this work, we present Tractable Uncertainty for STructure learning (TRUST), a framework for approximate posterior inference that relies on probabilistic circuits as a representation of our posterior belief. In contrast to sample-based posterior approximations, our representation can capture a much richer space of DAGs, while being able to tractably answer a range of useful inference queries. We empirically demonstrate how probabilistic circuits can be used to as an augmented representation for structure learning methods, leading to improvement in both the quality of inferred structures and posterior uncertainty. Experimental results also demonstrate the improved representational capacity of TRUST, outperforming competing methods on conditional query answering.

Deep learning has achieved tremendous success in designing novel chemical compounds with desirable pharmaceutical properties. In this work, we focus on a new type of drug design problem --- generating a small ``linker'' to physically attach two independent molecules with their distinct functions. The main computational challenges include: 1) the generation of linkers is conditional on the two given molecules, in contrast to generating complete molecules from scratch in previous works; 2) linkers heavily depend on the anchor atoms of the two molecules to be connected, which are not known beforehand; 3) 3D structures and orientations of the molecules need to be considered to avoid atom clashes, for which equivariance to E(3) group are necessary. To address these problems, we propose a conditional generative model, named 3DLinker, which is able to predict anchor atoms and jointly generate linker graphs and their 3D structures based on an E(3) equivariant graph variational autoencoder. So far as we know, no previous models could achieve this task. We compare our model with multiple conditional generative models modified from other molecular design tasks and find that our model has a significantly higher rate in recovering molecular graphs, and more importantly, accurately predicting the 3D coordinates of all the atoms.

We develop algorithms for imitation learning from policy data that was corrupted by temporally correlated noise in expert actions. When noise affects multiple timesteps of recorded data, it can manifest as spurious correlations between states and actions that a learner might latch on to, leading to poor policy performance. To break up these spurious correlations, we apply modern variants of the instrumental variable regression (IVR) technique of econometrics, enabling us to recover the underlying policy without requiring access to an interactive expert. In particular, we present two techniques, one of a generative-modeling flavor (DoubIL) that can utilize access to a simulator, and one of a game-theoretic flavor (ResiduIL) that can be run entirely offline. We find both of our algorithms compare favorably to behavioral cloning on simulated control tasks.

Offline RL algorithms must account for the fact that the dataset they are provided may leave many facets of the environment unknown. The most common way to approach this challenge is to employ pessimistic or conservative methods, which avoid behaviors that are too dissimilar from those in the training dataset. However, relying exclusively on conservatism has drawbacks: performance is sensitive to the exact degree of conservatism, and conservative objectives can recover highly suboptimal policies. In this work, we propose that offline RL methods should instead be adaptive in the presence of uncertainty. We show that acting optimally in offline RL in a Bayesian sense involves solving an implicit POMDP. As a result, optimal policies for offline RL must be adaptive, depending not just on the current state but rather all the transitions seen so far during evaluation. We present a model-free algorithm for approximating this optimal adaptive policy, and demonstrate the efficacy of learning such adaptive policies in offline RL benchmarks.

We analyze continuous-time models of accelerated gradient methods through deriving conservation laws in dilated coordinate systems. Namely, instead of analyzing the dynamics of $X(t)$, we analyze the dynamics of $W(t)=t^\alpha(X(t)-X_c)$ for some $\alpha$ and $X_c$ and derive a conserved quantity, analogous to physical energy, in this dilated coordinate system. Through this methodology, we recover many known continuous-time analyses in a streamlined manner and obtain novel continuous-time analyses for OGM-G, an acceleration mechanism for efficiently reducing gradient magnitude that is distinct from that of Nesterov. Finally, we show that a semi-second-order symplectic Euler discretization in the dilated coordinate system leads to an $\mathcal{O}(1/k^2)$ rate on the standard setup of smooth convex minimization, without any further assumptions such as infinite differentiability.

How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive approach to this foundational question, automatically encoding Occam's razor. Although it has been observed that the marginal likelihood can overfit and is sensitive to prior assumptions, its limitations for hyperparameter learning and discrete model comparison have not been thoroughly investigated. We first revisit the appealing properties of the marginal likelihood for learning constraints and hypothesis testing. We then highlight the conceptual and practical issues in using the marginal likelihood as a proxy for generalization. Namely, we show how marginal likelihood can be negatively correlated with generalization, with implications for neural architecture search, and can lead to both underfitting and overfitting in hyperparameter learning. We provide a partial remedy through a conditional marginal likelihood, which we show is more aligned with generalization, and practically valuable for large-scale hyperparameter learning, such as in deep kernel learning.