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Yuejie Chi

Publications and source records attributed to Yuejie Chi.

At least 73 records · Page 4Linked to original sources
arXiv2023

Identification of Nonlinear Latent Hierarchical Models

Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be highly challenging, especially when observed variables are generated by causally related latent variables and the relationships are nonlinear. In this work, we investigate the identification problem for nonlinear latent hierarchical causal models in which observed variables are generated by a set of causally related latent variables, and some latent variables may not have observed children. We show that the identifiability of causal structures and latent variables (up to invertible transformations) can be achieved under mild assumptions: on causal structures, we allow for multiple paths between any pair of variables in the graph, which relaxes latent tree assumptions in prior work; on structural functions, we permit general nonlinearity and multi-dimensional continuous variables, alleviating existing work's parametric assumptions. Specifically, we first develop an identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. Leveraging this criterion, we show that both causal structures and latent variables of the hierarchical model can be identified asymptotically by explicitly constructing an estimation procedure. To the best of our knowledge, our work is the first to establish identifiability guarantees for both causal structures and latent variables in nonlinear latent hierarchical models.

cs.LG↗
arXiv2023

Escaping Saddle Points in Heterogeneous Federated Learning via Distributed SGD with Communication Compression

We consider the problem of finding second-order stationary points of heterogeneous federated learning (FL). Previous works in FL mostly focus on first-order convergence guarantees, which do not rule out the scenario of unstable saddle points. Meanwhile, it is a key bottleneck of FL to achieve communication efficiency without compensating the learning accuracy, especially when local data are highly heterogeneous across different clients. Given this, we propose a novel algorithm Power-EF that only communicates compressed information via a novel error-feedback scheme. To our knowledge, Power-EF is the first distributed and compressed SGD algorithm that provably escapes saddle points in heterogeneous FL without any data homogeneity assumptions. In particular, Power-EF improves to second-order stationary points after visiting first-order (possibly saddle) points, using additional gradient queries and communication rounds only of almost the same order required by first-order convergence, and the convergence rate exhibits a linear speedup in terms of the number of workers. Our theory improves/recovers previous results, while extending to much more tolerant settings on the local data. Numerical experiments are provided to complement the theory.

cs.LG↗
arXiv2023

Seeing is not Believing: Robust Reinforcement Learning against Spurious Correlation

Robustness has been extensively studied in reinforcement learning (RL) to handle various forms of uncertainty such as random perturbations, rare events, and malicious attacks. In this work, we consider one critical type of robustness against spurious correlation, where different portions of the state do not have correlations induced by unobserved confounders. These spurious correlations are ubiquitous in real-world tasks, for instance, a self-driving car usually observes heavy traffic in the daytime and light traffic at night due to unobservable human activity. A model that learns such useless or even harmful correlation could catastrophically fail when the confounder in the test case deviates from the training one. Although motivated, enabling robustness against spurious correlation poses significant challenges since the uncertainty set, shaped by the unobserved confounder and causal structure, is difficult to characterize and identify. Existing robust algorithms that assume simple and unstructured uncertainty sets are therefore inadequate to address this challenge. To solve this issue, we propose Robust State-Confounded Markov Decision Processes (RSC-MDPs) and theoretically demonstrate its superiority in avoiding learning spurious correlations compared with other robust RL counterparts. We also design an empirical algorithm to learn the robust optimal policy for RSC-MDPs, which outperforms all baselines in eight realistic self-driving and manipulation tasks.

cs.LG↗
arXiv2023

Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterization

Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor factorization, one of the most popular approaches is to employ simple iterative algorithms such as gradient descent (GD) to recover the low-rank factors directly, which allow for small memory and computation footprints. However, the convergence rate of GD depends linearly, and sometimes even quadratically, on the condition number of the low-rank object, and therefore, GD slows down painstakingly when the problem is ill-conditioned. This chapter introduces a new algorithmic approach, dubbed scaled gradient descent (ScaledGD), that provably converges linearly at a constant rate independent of the condition number of the low-rank object, while maintaining the low per-iteration cost of gradient descent for a variety of tasks including sensing, robust principal component analysis and completion. In addition, ScaledGD continues to admit fast global convergence to the minimax-optimal solution, again almost independent of the condition number, from a small random initialization when the rank is over-specified in the presence of Gaussian noise. In total, ScaledGD highlights the power of appropriate preconditioning in accelerating nonconvex statistical estimation, where the iteration-varying preconditioners promote desirable invariance properties of the trajectory with respect to the symmetry in low-rank factorization without hurting generalization.

cs.LG↗
arXiv2023

Global Convergence of Policy Gradient Methods in Reinforcement Learning, Games and Control

Policy gradient methods, where one searches for the policy of interest by maximizing the value functions using first-order information, become increasingly popular for sequential decision making in reinforcement learning, games, and control. Guaranteeing the global optimality of policy gradient methods, however, is highly nontrivial due to nonconcavity of the value functions. In this exposition, we highlight recent progresses in understanding and developing policy gradient methods with global convergence guarantees, putting an emphasis on their finite-time convergence rates with regard to salient problem parameters.

math.OC↗
arXiv2023

A Lightweight Transformer for Faster and Robust EBSD Data Collection

Three dimensional electron back-scattered diffraction (EBSD) microscopy is a critical tool in many applications in materials science, yet its data quality can fluctuate greatly during the arduous collection process, particularly via serial-sectioning. Fortunately, 3D EBSD data is inherently sequential, opening up the opportunity to use transformers, state-of-the-art deep learning architectures that have made breakthroughs in a plethora of domains, for data processing and recovery. To be more robust to errors and accelerate this 3D EBSD data collection, we introduce a two step method that recovers missing slices in an 3D EBSD volume, using an efficient transformer model and a projection algorithm to process the transformer's outputs. Overcoming the computational and practical hurdles of deep learning with scarce high dimensional data, we train this model using only synthetic 3D EBSD data with self-supervision and obtain superior recovery accuracy on real 3D EBSD data, compared to existing methods.

cs.CV↗
arXiv2023

Offline Reinforcement Learning with On-Policy Q-Function Regularization

The core challenge of offline reinforcement learning (RL) is dealing with the (potentially catastrophic) extrapolation error induced by the distribution shift between the history dataset and the desired policy. A large portion of prior work tackles this challenge by implicitly/explicitly regularizing the learning policy towards the behavior policy, which is hard to estimate reliably in practice. In this work, we propose to regularize towards the Q-function of the behavior policy instead of the behavior policy itself, under the premise that the Q-function can be estimated more reliably and easily by a SARSA-style estimate and handles the extrapolation error more straightforwardly. We propose two algorithms taking advantage of the estimated Q-function through regularizations, and demonstrate they exhibit strong performance on the D4RL benchmarks.

cs.LG↗
arXiv2023

Understanding Masked Autoencoders via Hierarchical Latent Variable Models

Masked autoencoder (MAE), a simple and effective self-supervised learning framework based on the reconstruction of masked image regions, has recently achieved prominent success in a variety of vision tasks. Despite the emergence of intriguing empirical observations on MAE, a theoretically principled understanding is still lacking. In this work, we formally characterize and justify existing empirical insights and provide theoretical guarantees of MAE. We formulate the underlying data-generating process as a hierarchical latent variable model and show that under reasonable assumptions, MAE provably identifies a set of latent variables in the hierarchical model, explaining why MAE can extract high-level information from pixels. Further, we show how key hyperparameters in MAE (the masking ratio and the patch size) determine which true latent variables to be recovered, therefore influencing the level of semantic information in the representation. Specifically, extremely large or small masking ratios inevitably lead to low-level representations. Our theory offers coherent explanations of existing empirical observations and provides insights for potential empirical improvements and fundamental limitations of the masking-reconstruction paradigm. We conduct extensive experiments to validate our theoretical insights.

cs.LG↗
arXiv2023

Convergence and Privacy of Decentralized Nonconvex Optimization with Gradient Clipping and Communication Compression

Achieving communication efficiency in decentralized machine learning has been attracting significant attention, with communication compression recognized as an effective technique in algorithm design. This paper takes a first step to understand the role of gradient clipping, a popular strategy in practice, in decentralized nonconvex optimization with communication compression. We propose PORTER, which considers two variants of gradient clipping added before or after taking a mini-batch of stochastic gradients, where the former variant PORTER-DP allows local differential privacy analysis with additional Gaussian perturbation, and the latter variant PORTER-GC helps to stabilize training. We develop a novel analysis framework that establishes their convergence guarantees without assuming the stringent bounded gradient assumption. To the best of our knowledge, our work provides the first convergence analysis for decentralized nonconvex optimization with gradient clipping and communication compression, highlighting the trade-offs between convergence rate, compression ratio, network connectivity, and privacy.

cs.LG↗
arXiv2023

Reward-agnostic Fine-tuning: Provable Statistical Benefits of Hybrid Reinforcement Learning

This paper studies tabular reinforcement learning (RL) in the hybrid setting, which assumes access to both an offline dataset and online interactions with the unknown environment. A central question boils down to how to efficiently utilize online data collection to strengthen and complement the offline dataset and enable effective policy fine-tuning. Leveraging recent advances in reward-agnostic exploration and model-based offline RL, we design a three-stage hybrid RL algorithm that beats the best of both worlds -- pure offline RL and pure online RL -- in terms of sample complexities. The proposed algorithm does not require any reward information during data collection. Our theory is developed based on a new notion called single-policy partial concentrability, which captures the trade-off between distribution mismatch and miscoverage and guides the interplay between offline and online data.

cs.LG↗
arXiv2023

Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model

This paper is concerned with the sample efficiency of reinforcement learning, assuming access to a generative model (or simulator). We first consider $γ$-discounted infinite-horizon Markov decision processes (MDPs) with state space $\mathcal{S}$ and action space $\mathcal{A}$. Despite a number of prior works tackling this problem, a complete picture of the trade-offs between sample complexity and statistical accuracy is yet to be determined. In particular, all prior results suffer from a severe sample size barrier, in the sense that their claimed statistical guarantees hold only when the sample size exceeds at least $\frac{|\mathcal{S}||\mathcal{A}|}{(1-γ)^2}$. The current paper overcomes this barrier by certifying the minimax optimality of two algorithms -- a perturbed model-based algorithm and a conservative model-based algorithm -- as soon as the sample size exceeds the order of $\frac{|\mathcal{S}||\mathcal{A}|}{1-γ}$ (modulo some log factor). Moving beyond infinite-horizon MDPs, we further study time-inhomogeneous finite-horizon MDPs, and prove that a plain model-based planning algorithm suffices to achieve minimax-optimal sample complexity given any target accuracy level. To the best of our knowledge, this work delivers the first minimax-optimal guarantees that accommodate the entire range of sample sizes (beyond which finding a meaningful policy is information theoretically infeasible).

cs.LG↗
arXiv2023

Is Q-Learning Minimax Optimal? A Tight Sample Complexity Analysis

Q-learning, which seeks to learn the optimal Q-function of a Markov decision process (MDP) in a model-free fashion, lies at the heart of reinforcement learning. When it comes to the synchronous setting (such that independent samples for all state-action pairs are drawn from a generative model in each iteration), substantial progress has been made towards understanding the sample efficiency of Q-learning. Consider a $γ$-discounted infinite-horizon MDP with state space $\mathcal{S}$ and action space $\mathcal{A}$: to yield an entrywise $\varepsilon$-approximation of the optimal Q-function, state-of-the-art theory for Q-learning requires a sample size exceeding the order of $\frac{|\mathcal{S}||\mathcal{A}|}{(1-γ)^5\varepsilon^{2}}$, which fails to match existing minimax lower bounds. This gives rise to natural questions: what is the sharp sample complexity of Q-learning? Is Q-learning provably sub-optimal? This paper addresses these questions for the synchronous setting: (1) when $|\mathcal{A}|=1$ (so that Q-learning reduces to TD learning), we prove that the sample complexity of TD learning is minimax optimal and scales as $\frac{|\mathcal{S}|}{(1-γ)^3\varepsilon^2}$ (up to log factor); (2) when $|\mathcal{A}|\geq 2$, we settle the sample complexity of Q-learning to be on the order of $\frac{|\mathcal{S}||\mathcal{A}|}{(1-γ)^4\varepsilon^2}$ (up to log factor). Our theory unveils the strict sub-optimality of Q-learning when $|\mathcal{A}|\geq 2$, and rigorizes the negative impact of over-estimation in Q-learning. Finally, we extend our analysis to accommodate asynchronous Q-learning (i.e., the case with Markovian samples), sharpening the horizon dependency of its sample complexity to be $\frac{1}{(1-γ)^4}$.

stat.ML↗
arXiv2023

Local Geometry of Nonconvex Spike Deconvolution from Low-Pass Measurements

Spike deconvolution is the problem of recovering the point sources from their convolution with a known point spread function, which plays a fundamental role in many sensing and imaging applications. In this paper, we investigate the local geometry of recovering the parameters of point sources$\unicode{x2014}$including both amplitudes and locations$\unicode{x2014}$by minimizing a natural nonconvex least-squares loss function measuring the observation residuals. We propose preconditioned variants of gradient descent (GD), where the search direction is scaled via some carefully designed preconditioning matrices. We begin with a simple fixed preconditioner design, which adjusts the learning rates of the locations at a different scale from those of the amplitudes, and show it achieves a linear rate of convergence$\unicode{x2014}$in terms of entrywise errors$\unicode{x2014}$when initialized close to the ground truth, as long as the separation between the true spikes is sufficiently large. However, the convergence rate slows down significantly when the dynamic range of the source amplitudes is large. To bridge this issue, we introduce an adaptive preconditioner design, which compensates for the learning rates of different sources in an iteration-varying manner based on the current estimate. The adaptive design provably leads to an accelerated convergence rate that is independent of the dynamic range, highlighting the benefit of adaptive preconditioning in nonconvex spike deconvolution. Numerical experiments are provided to corroborate the theoretical findings.

cs.IT↗
arXiv2023

Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descent

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key challenge is to develop computationally efficient and provably correct algorithms for extracting useful information from tensor data that are simultaneously robust to corruptions and ill-conditioning. This paper tackles tensor robust principal component analysis (RPCA), which aims to recover a low-rank tensor from its observations contaminated by sparse corruptions, under the Tucker decomposition. To minimize the computation and memory footprints, we propose to directly recover the low-dimensional tensor factors -- starting from a tailored spectral initialization -- via scaled gradient descent (ScaledGD), coupled with an iteration-varying thresholding operation to adaptively remove the impact of corruptions. Theoretically, we establish that the proposed algorithm converges linearly to the true low-rank tensor at a constant rate that is independent with its condition number, as long as the level of corruptions is not too large. Empirically, we demonstrate that the proposed algorithm achieves better and more scalable performance than state-of-the-art matrix and tensor RPCA algorithms through synthetic experiments and real-world applications.

stat.ML↗
arXiv2023

Fast Policy Extragradient Methods for Competitive Games with Entropy Regularization

This paper investigates the problem of computing the equilibrium of competitive games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding the last-iterate convergence of extragradient methods in the unconstrained setting, the theoretical underpinnings of these methods in the constrained settings, especially those using multiplicative updates, remain highly inadequate, even when the objective function is bilinear. Motivated by the algorithmic role of entropy regularization in single-agent reinforcement learning and game theory, we develop provably efficient extragradient methods to find the quantal response equilibrium (QRE) -- which are solutions to zero-sum two-player matrix games with entropy regularization -- at a linear rate. The proposed algorithms can be implemented in a decentralized manner, where each player executes symmetric and multiplicative updates iteratively using its own payoff without observing the opponent's actions directly. In addition, by controlling the knob of entropy regularization, the proposed algorithms can locate an approximate Nash equilibrium of the unregularized matrix game at a sublinear rate without assuming the Nash equilibrium to be unique. Our methods also lead to efficient policy extragradient algorithms for solving (entropy-regularized) zero-sum Markov games at similar rates. All of our convergence rates are nearly dimension-free, which are independent of the size of the state and action spaces up to logarithm factors, highlighting the positive role of entropy regularization for accelerating convergence.

math.OC↗
arXiv2023

Policy Mirror Descent for Regularized Reinforcement Learning: A Generalized Framework with Linear Convergence

Policy optimization, which finds the desired policy by maximizing value functions via optimization techniques, lies at the heart of reinforcement learning (RL). In addition to value maximization, other practical considerations arise as well, including the need of encouraging exploration, and that of ensuring certain structural properties of the learned policy due to safety, resource and operational constraints. These can often be accounted for via regularized RL, which augments the target value function with a structure-promoting regularizer. Focusing on discounted infinite-horizon Markov decision processes, we propose a generalized policy mirror descent (GPMD) algorithm for solving regularized RL. As a generalization of policy mirror descent (arXiv:2102.00135), our algorithm accommodates a general class of convex regularizers and promotes the use of Bregman divergence in cognizant of the regularizer in use. We demonstrate that our algorithm converges linearly to the global solution over an entire range of learning rates, in a dimension-free fashion, even when the regularizer lacks strong convexity and smoothness. In addition, this linear convergence feature is provably stable in the face of inexact policy evaluation and imperfect policy updates. Numerical experiments are provided to corroborate the appealing performance of GPMD.

cs.LG↗
arXiv2022

Deep Unfolded Tensor Robust PCA with Self-supervised Learning

Tensor robust principal component analysis (RPCA), which seeks to separate a low-rank tensor from its sparse corruptions, has been crucial in data science and machine learning where tensor structures are becoming more prevalent. While powerful, existing tensor RPCA algorithms can be difficult to use in practice, as their performance can be sensitive to the choice of additional hyperparameters, which are not straightforward to tune. In this paper, we describe a fast and simple self-supervised model for tensor RPCA using deep unfolding by only learning four hyperparameters. Despite its simplicity, our model expunges the need for ground truth labels while maintaining competitive or even greater performance compared to supervised deep unfolding. Furthermore, our model is capable of operating in extreme data-starved scenarios. We demonstrate these claims on a mix of synthetic data and real-world tasks, comparing performance against previously studied supervised deep unfolding methods and Bayesian optimization baselines.

stat.ML↗
arXiv2022

Softmax Policy Gradient Methods Can Take Exponential Time to Converge

The softmax policy gradient (PG) method, which performs gradient ascent under softmax policy parameterization, is arguably one of the de facto implementations of policy optimization in modern reinforcement learning. For $γ$-discounted infinite-horizon tabular Markov decision processes (MDPs), remarkable progress has recently been achieved towards establishing global convergence of softmax PG methods in finding a near-optimal policy. However, prior results fall short of delineating clear dependencies of convergence rates on salient parameters such as the cardinality of the state space $\mathcal{S}$ and the effective horizon $\frac{1}{1-γ}$, both of which could be excessively large. In this paper, we deliver a pessimistic message regarding the iteration complexity of softmax PG methods, despite assuming access to exact gradient computation. Specifically, we demonstrate that the softmax PG method with stepsize $η$ can take \[ \frac{1}η |\mathcal{S}|^{2^{Ω\big(\frac{1}{1-γ}\big)}} ~\text{iterations} \] to converge, even in the presence of a benign policy initialization and an initial state distribution amenable to exploration (so that the distribution mismatch coefficient is not exceedingly large). This is accomplished by characterizing the algorithmic dynamics over a carefully-constructed MDP containing only three actions. Our exponential lower bound hints at the necessity of carefully adjusting update rules or enforcing proper regularization in accelerating PG methods.

cs.LG↗