arXiv subjects

Mengdi Wang

Publications and source records attributed to Mengdi Wang.

At least 235 records · Page 13Linked to original sources

arXiv2022

Parameter-Efficient Sparsity for Large Language Models Fine-Tuning

With the dramatically increased number of parameters in language models, sparsity methods have received ever-increasing research focus to compress and accelerate the models. While most research focuses on how to accurately retain appropriate weights while maintaining the performance of the compressed model, there are challenges in the computational overhead and memory footprint of sparse training when compressing large-scale language models. To address this problem, we propose a Parameter-efficient Sparse Training (PST) method to reduce the number of trainable parameters during sparse-aware training in downstream tasks. Specifically, we first combine the data-free and data-driven criteria to efficiently and accurately measure the importance of weights. Then we investigate the intrinsic redundancy of data-driven weight importance and derive two obvious characteristics i.e., low-rankness and structuredness. Based on that, two groups of small matrices are introduced to compute the data-driven importance of weights, instead of using the original large importance score matrix, which therefore makes the sparse training resource-efficient and parameter-efficient. Experiments with diverse networks (i.e., BERT, RoBERTa and GPT-2) on dozens of datasets demonstrate PST performs on par or better than previous sparsity methods, despite only training a small number of parameters. For instance, compared with previous sparsity methods, our PST only requires 1.5% trainable parameters to achieve comparable performance on BERT.

cs.AI↗

arXiv2022

Bootstrapping Fitted Q-Evaluation for Off-Policy Inference

Bootstrapping provides a flexible and effective approach for assessing the quality of batch reinforcement learning, yet its theoretical property is less understood. In this paper, we study the use of bootstrapping in off-policy evaluation (OPE), and in particular, we focus on the fitted Q-evaluation (FQE) that is known to be minimax-optimal in the tabular and linear-model cases. We propose a bootstrapping FQE method for inferring the distribution of the policy evaluation error and show that this method is asymptotically efficient and distributionally consistent for off-policy statistical inference. To overcome the computation limit of bootstrapping, we further adapt a subsampling procedure that improves the runtime by an order of magnitude. We numerically evaluate the bootrapping method in classical RL environments for confidence interval estimation, estimating the variance of off-policy evaluator, and estimating the correlation between multiple off-policy evaluators.

stat.ML↗

arXiv2022

Near-optimal Offline Reinforcement Learning with Linear Representation: Leveraging Variance Information with Pessimism

Offline reinforcement learning, which seeks to utilize offline/historical data to optimize sequential decision-making strategies, has gained surging prominence in recent studies. Due to the advantage that appropriate function approximators can help mitigate the sample complexity burden in modern reinforcement learning problems, existing endeavors usually enforce powerful function representation models (e.g. neural networks) to learn the optimal policies. However, a precise understanding of the statistical limits with function representations, remains elusive, even when such a representation is linear. Towards this goal, we study the statistical limits of offline reinforcement learning with linear model representations. To derive the tight offline learning bound, we design the variance-aware pessimistic value iteration (VAPVI), which adopts the conditional variance information of the value function for time-inhomogeneous episodic linear Markov decision processes (MDPs). VAPVI leverages estimated variances of the value functions to reweight the Bellman residuals in the least-square pessimistic value iteration and provides improved offline learning bounds over the best-known existing results (whereas the Bellman residuals are equally weighted by design). More importantly, our learning bounds are expressed in terms of system quantities, which provide natural instance-dependent characterizations that previous results are short of. We hope our results draw a clearer picture of what offline learning should look like when linear representations are provided.

cs.LG↗

arXiv2022

Off-Policy Fitted Q-Evaluation with Differentiable Function Approximators: Z-Estimation and Inference Theory

Off-Policy Evaluation (OPE) serves as one of the cornerstones in Reinforcement Learning (RL). Fitted Q Evaluation (FQE) with various function approximators, especially deep neural networks, has gained practical success. While statistical analysis has proved FQE to be minimax-optimal with tabular, linear and several nonparametric function families, its practical performance with more general function approximator is less theoretically understood. We focus on FQE with general differentiable function approximators, making our theory applicable to neural function approximations. We approach this problem using the Z-estimation theory and establish the following results: The FQE estimation error is asymptotically normal with explicit variance determined jointly by the tangent space of the function class at the ground truth, the reward structure, and the distribution shift due to off-policy learning; The finite-sample FQE error bound is dominated by the same variance term, and it can also be bounded by function class-dependent divergence, which measures how the off-policy distribution shift intertwines with the function approximator. In addition, we study bootstrapping FQE estimators for error distribution inference and estimating confidence intervals, accompanied by a Cramer-Rao lower bound that matches our upper bounds. The Z-estimation analysis provides a generalizable theoretical framework for studying off-policy estimation in RL and provides sharp statistical theory for FQE with differentiable function approximators.

stat.ML↗

arXiv2021

Optimal policy evaluation using kernel-based temporal difference methods

We study methods based on reproducing kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process (MRP). We study a regularized form of the kernel least-squares temporal difference (LSTD) estimate; in the population limit of infinite data, it corresponds to the fixed point of a projected Bellman operator defined by the associated reproducing kernel Hilbert space. The estimator itself is obtained by computing the projected fixed point induced by a regularized version of the empirical operator; due to the underlying kernel structure, this reduces to solving a linear system involving kernel matrices. We analyze the error of this estimate in the $L^2(μ)$-norm, where $μ$ denotes the stationary distribution of the underlying Markov chain. Our analysis imposes no assumptions on the transition operator of the Markov chain, but rather only conditions on the reward function and population-level kernel LSTD solutions. We use empirical process theory techniques to derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator, as well as the instance-dependent variance of the Bellman residual error. In addition, we prove minimax lower bounds over sub-classes of MRPs, which shows that our rate is optimal in terms of the sample size $n$ and the effective horizon $H = (1 - γ)^{-1}$. Whereas existing worst-case theory predicts cubic scaling ($H^3$) in the effective horizon, our theory reveals that there is in fact a much wider range of scalings, depending on the kernel, the stationary distribution, and the variance of the Bellman residual error. Notably, it is only parametric and near-parametric problems that can ever achieve the worst-case cubic scaling.

stat.ML↗

arXiv2021

High-Dimensional Sparse Linear Bandits

Stochastic linear bandits with high-dimensional sparse features are a practical model for a variety of domains, including personalized medicine and online advertising. We derive a novel $Ω(n^{2/3})$ dimension-free minimax regret lower bound for sparse linear bandits in the data-poor regime where the horizon is smaller than the ambient dimension and where the feature vectors admit a well-conditioned exploration distribution. This is complemented by a nearly matching upper bound for an explore-then-commit algorithm showing that that $Θ(n^{2/3})$ is the optimal rate in the data-poor regime. The results complement existing bounds for the data-rich regime and provide another example where carefully balancing the trade-off between information and regret is necessary. Finally, we prove a dimension-free $O(\sqrt{n})$ regret upper bound under an additional assumption on the magnitude of the signal for relevant features.

stat.ML↗

arXiv2021

Boosting the Convergence of Reinforcement Learning-based Auto-pruning Using Historical Data

Recently, neural network compression schemes like channel pruning have been widely used to reduce the model size and computational complexity of deep neural network (DNN) for applications in power-constrained scenarios such as embedded systems. Reinforcement learning (RL)-based auto-pruning has been further proposed to automate the DNN pruning process to avoid expensive hand-crafted work. However, the RL-based pruner involves a time-consuming training process and the high expense of each sample further exacerbates this problem. These impediments have greatly restricted the real-world application of RL-based auto-pruning. Thus, in this paper, we propose an efficient auto-pruning framework which solves this problem by taking advantage of the historical data from the previous auto-pruning process. In our framework, we first boost the convergence of the RL-pruner by transfer learning. Then, an augmented transfer learning scheme is proposed to further speed up the training process by improving the transferability. Finally, an assistant learning process is proposed to improve the sample efficiency of the RL agent. The experiments have shown that our framework can accelerate the auto-pruning process by 1.5-2.5 times for ResNet20, and 1.81-2.375 times for other neural networks like ResNet56, ResNet18, and MobileNet v1.

cs.LG↗

arXiv2021

MARL with General Utilities via Decentralized Shadow Reward Actor-Critic

We posit a new mechanism for cooperation in multi-agent reinforcement learning (MARL) based upon any nonlinear function of the team's long-term state-action occupancy measure, i.e., a \emph{general utility}. This subsumes the cumulative return but also allows one to incorporate risk-sensitivity, exploration, and priors. % We derive the {\bf D}ecentralized {\bf S}hadow Reward {\bf A}ctor-{\bf C}ritic (DSAC) in which agents alternate between policy evaluation (critic), weighted averaging with neighbors (information mixing), and local gradient updates for their policy parameters (actor). DSAC augments the classic critic step by requiring agents to (i) estimate their local occupancy measure in order to (ii) estimate the derivative of the local utility with respect to their occupancy measure, i.e., the "shadow reward". DSAC converges to $ε$-stationarity in $\mathcal{O}(1/ε^{2.5})$ (Theorem \ref{theorem:final}) or faster $\mathcal{O}(1/ε^{2})$ (Corollary \ref{corollary:communication}) steps with high probability, depending on the amount of communications. We further establish the non-existence of spurious stationary points for this problem, that is, DSAC finds the globally optimal policy (Corollary \ref{corollary:global}). Experiments demonstrate the merits of goals beyond the cumulative return in cooperative MARL.

stat.ML↗

arXiv2021

You Only Compress Once: Towards Effective and Elastic BERT Compression via Exploit-Explore Stochastic Nature Gradient

Despite superior performance on various natural language processing tasks, pre-trained models such as BERT are challenged by deploying on resource-constraint devices. Most existing model compression approaches require re-compression or fine-tuning across diverse constraints to accommodate various hardware deployments. This practically limits the further application of model compression. Moreover, the ineffective training and searching process of existing elastic compression paradigms[4,27] prevents the direct migration to BERT compression. Motivated by the necessity of efficient inference across various constraints on BERT, we propose a novel approach, YOCO-BERT, to achieve compress once and deploy everywhere. Specifically, we first construct a huge search space with 10^13 architectures, which covers nearly all configurations in BERT model. Then, we propose a novel stochastic nature gradient optimization method to guide the generation of optimal candidate architecture which could keep a balanced trade-off between explorations and exploitation. When a certain resource constraint is given, a lightweight distribution optimization approach is utilized to obtain the optimal network for target deployment without fine-tuning. Compared with state-of-the-art algorithms, YOCO-BERT provides more compact models, yet achieving 2.1%-4.5% average accuracy improvement on the GLUE benchmark. Besides, YOCO-BERT is also more effective, e.g.,the training complexity is O(1)for N different devices. Code is availablehttps://github.com/MAC-AutoML/YOCO-BERT.

cs.CL↗

arXiv2021

On the Convergence and Sample Efficiency of Variance-Reduced Policy Gradient Method

Policy gradient (PG) gives rise to a rich class of reinforcement learning (RL) methods. Recently, there has been an emerging trend to accelerate the existing PG methods such as REINFORCE by the \emph{variance reduction} techniques. However, all existing variance-reduced PG methods heavily rely on an uncheckable importance weight assumption made for every single iteration of the algorithms. In this paper, a simple gradient truncation mechanism is proposed to address this issue. Moreover, we design a Truncated Stochastic Incremental Variance-Reduced Policy Gradient (TSIVR-PG) method, which is able to maximize not only a cumulative sum of rewards but also a general utility function over a policy's long-term visiting distribution. We show an $\tilde{\mathcal{O}}(ε^{-3})$ sample complexity for TSIVR-PG to find an $ε$-stationary policy. By assuming the overparameterizaiton of policy and exploiting the hidden convexity of the problem, we further show that TSIVR-PG converges to global $ε$-optimal policy with $\tilde{\mathcal{O}}(ε^{-2})$ samples.

cs.LG↗

arXiv2021

Towards Compact CNNs via Collaborative Compression

Channel pruning and tensor decomposition have received extensive attention in convolutional neural network compression. However, these two techniques are traditionally deployed in an isolated manner, leading to significant accuracy drop when pursuing high compression rates. In this paper, we propose a Collaborative Compression (CC) scheme, which joints channel pruning and tensor decomposition to compress CNN models by simultaneously learning the model sparsity and low-rankness. Specifically, we first investigate the compression sensitivity of each layer in the network, and then propose a Global Compression Rate Optimization that transforms the decision problem of compression rate into an optimization problem. After that, we propose multi-step heuristic compression to remove redundant compression units step-by-step, which fully considers the effect of the remaining compression space (i.e., unremoved compression units). Our method demonstrates superior performance gains over previous ones on various datasets and backbone architectures. For example, we achieve 52.9% FLOPs reduction by removing 48.4% parameters on ResNet-50 with only a Top-1 accuracy drop of 0.56% on ImageNet 2012.

cs.CV↗

arXiv2021

Contrastive Multi-document Question Generation

Multi-document question generation focuses on generating a question that covers the common aspect of multiple documents. Such a model is useful in generating clarifying options. However, a naive model trained only using the targeted ("positive") document set may generate too generic questions that cover a larger scope than delineated by the document set. To address this challenge, we introduce the contrastive learning strategy where given "positive" and "negative" sets of documents, we generate a question that is closely related to the "positive" set but is far away from the "negative" set. This setting allows generated questions to be more specific and related to the target document set. To generate such specific questions, we propose Multi-Source Coordinated Question Generator (MSCQG), a novel framework that includes a supervised learning (SL) stage and a reinforcement learning (RL) stage. In the SL stage, a single-document question generator is trained. In the RL stage, a coordinator model is trained to find optimal attention weights to align multiple single-document generators, by optimizing a reward designed to promote specificity of generated questions. We also develop an effective auxiliary objective, named Set-induced Contrastive Regularization (SCR) that improves the coordinator's contrastive learning during the RL stage. We show that our model significantly outperforms several strong baselines, as measured by automatic metrics and human evaluation. The source repository is publicly available at \url{www.github.com/woonsangcho/contrast_qgen}.

cs.CL↗

arXiv2021

Thin-Film Smoothed Particle Hydrodynamics Fluid

We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with the dimensionality reduced using the asymptotic lubrication theory and customize a set of differential operators based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) for evolving pointset surfaces. The key insight is that the compressible nature of SPH, which is unfavorable in its typical usage, is helpful in our application to co-evolve the thickness, calculate the surface tension, and enforce the fluid incompressibility on a thin film. In this way, we are able to two-way couple the surface deformation with the in-plane flows in a physically based manner. We can simulate complex vortical swirls, fingering effects due to Rayleigh-Taylor instability, capillary waves, Newton's interference fringes, and the Marangoni effect on liberally deforming surfaces by presenting both realistic visual results and numerical validations. The particle-based nature of our system also enables it to conveniently handle topology changes and codimension transitions, allowing us to marry the thin-film simulation with a wide gamut of 3D phenomena, such as pinch-off of unstable catenoids, dripping under gravity, merging of droplets, as well as bubble rupture.

physics.flu-dyn↗

arXiv2021

Online Sparse Reinforcement Learning

We investigate the hardness of online reinforcement learning in fixed horizon, sparse linear Markov decision process (MDP), with a special focus on the high-dimensional regime where the ambient dimension is larger than the number of episodes. Our contribution is two-fold. First, we provide a lower bound showing that linear regret is generally unavoidable in this case, even if there exists a policy that collects well-conditioned data. The lower bound construction uses an MDP with a fixed number of states while the number of actions scales with the ambient dimension. Note that when the horizon is fixed to one, the case of linear stochastic bandits, the linear regret can be avoided. Second, we show that if the learner has oracle access to a policy that collects well-conditioned data then a variant of Lasso fitted Q-iteration enjoys a nearly dimension-free regret of $\tilde{O}( s^{2/3} N^{2/3})$ where $N$ is the number of episodes and $s$ is the sparsity level. This shows that in the large-action setting, the difficulty of learning can be attributed to the difficulty of finding a good exploratory policy.

cs.LG↗

arXiv2020

On Function Approximation in Reinforcement Learning: Optimism in the Face of Large State Spaces

The classical theory of reinforcement learning (RL) has focused on tabular and linear representations of value functions. Further progress hinges on combining RL with modern function approximators such as kernel functions and deep neural networks, and indeed there have been many empirical successes that have exploited such combinations in large-scale applications. There are profound challenges, however, in developing a theory to support this enterprise, most notably the need to take into consideration the exploration-exploitation tradeoff at the core of RL in conjunction with the computational and statistical tradeoffs that arise in modern function-approximation-based learning systems. We approach these challenges by studying an optimistic modification of the least-squares value iteration algorithm, in the context of the action-value function represented by a kernel function or an overparameterized neural network. We establish both polynomial runtime complexity and polynomial sample complexity for this algorithm, without additional assumptions on the data-generating model. In particular, we prove that the algorithm incurs an $\tilde{\mathcal{O}}(δ_{\mathcal{F}} H^2 \sqrt{T})$ regret, where $δ_{\mathcal{F}}$ characterizes the intrinsic complexity of the function class $\mathcal{F}$, $H$ is the length of each episode, and $T$ is the total number of episodes. Our regret bounds are independent of the number of states, a result which exhibits clearly the benefit of function approximation in RL.

cs.LG↗

arXiv2020

Variance Reduced Value Iteration and Faster Algorithms for Solving Markov Decision Processes

In this paper we provide faster algorithms for approximately solving discounted Markov Decision Processes in multiple parameter regimes. Given a discounted Markov Decision Process (DMDP) with $|S|$ states, $|A|$ actions, discount factor $γ\in(0,1)$, and rewards in the range $[-M, M]$, we show how to compute an $ε$-optimal policy, with probability $1 - δ$ in time \[ \tilde{O}\left( \left(|S|^2 |A| + \frac{|S| |A|}{(1 - γ)^3} \right) \log\left( \frac{M}ε \right) \log\left( \frac{1}δ \right) \right) ~ . \] This contribution reflects the first nearly linear time, nearly linearly convergent algorithm for solving DMDPs for intermediate values of $γ$. We also show how to obtain improved sublinear time algorithms provided we can sample from the transition function in $O(1)$ time. Under this assumption we provide an algorithm which computes an $ε$-optimal policy with probability $1 - δ$ in time \[ \tilde{O} \left(\frac{|S| |A| M^2}{(1 - γ)^4 ε^2} \log \left(\frac{1}δ\right) \right) ~. \] Lastly, we extend both these algorithms to solve finite horizon MDPs. Our algorithms improve upon the previous best for approximately computing optimal policies for fixed-horizon MDPs in multiple parameter regimes. Interestingly, we obtain our results by a careful modification of approximate value iteration. We show how to combine classic approximate value iteration analysis with new techniques in variance reduction. Our fastest algorithms leverage further insights to ensure that our algorithms make monotonic progress towards the optimal value. This paper is one of few instances in using sampling to obtain a linearly convergent linear programming algorithm and we hope that the analysis may be useful more broadly.

cs.DS↗

arXiv2020

Learning Markov models via low-rank optimization

Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small rank despite of having a large state space, meaning that the system admits a low-dimensional latent structure. We show that one can estimate the full transition model accurately using a trajectory of length that is proportional to the total number of states. We propose two maximum likelihood estimation methods: a convex approach with nuclear-norm regularization and a nonconvex approach with rank constraint. We explicitly derive the statistical rates of both estimators in terms of the Kullback-Leiber divergence and the $\ell_2$ error and also establish a minimax lower bound to assess the tightness of these rates. For computing the nonconvex estimator, we develop a novel DC (difference of convex function) programming algorithm that starts with the convex M-estimator and then successively refines the solution till convergence. Empirical experiments demonstrate consistent superiority of the nonconvex estimator over the convex one.

stat.ME↗

arXiv2020

Sparse Feature Selection Makes Batch Reinforcement Learning More Sample Efficient

This paper provides a statistical analysis of high-dimensional batch Reinforcement Learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that sparsity-aware methods can make batch RL more sample efficient. We first consider the off-policy policy evaluation problem. To evaluate a new target policy, we analyze a Lasso fitted Q-evaluation method and establish a finite-sample error bound that has no polynomial dependence on the ambient dimension. To reduce the Lasso bias, we further propose a post model-selection estimator that applies fitted Q-evaluation to the features selected via group Lasso. Under an additional signal strength assumption, we derive a sharper instance-dependent error bound that depends on a divergence function measuring the distribution mismatch between the data distribution and occupancy measure of the target policy. Further, we study the Lasso fitted Q-iteration for batch policy optimization and establish a finite-sample error bound depending on the ratio between the number of relevant features and restricted minimal eigenvalue of the data's covariance. In the end, we complement the results with minimax lower bounds for batch-data policy evaluation/optimization that nearly match our upper bounds. The results suggest that having well-conditioned data is crucial for sparse batch policy learning.

cs.LG↗