Search Results for author: Guanghui Lan

Found 48 papers, 4 papers with code

Complexity of Training ReLU Neural Networks

no code implementations ICLR 2019 Digvijay Boob, Santanu S. Dey, Guanghui Lan

In this paper, we explore some basic questions on complexity of training Neural networks with ReLU activation function.

A simple uniformly optimal method without line search for convex optimization

no code implementations16 Oct 2023 Tianjiao Li, Guanghui Lan

Line search (or backtracking) procedures have been widely employed into first-order methods for solving convex optimization problems, especially those with unknown problem parameters (e. g., Lipschitz constant).

First-order Policy Optimization for Robust Policy Evaluation

no code implementations29 Jul 2023 Yan Li, Guanghui Lan

We adopt a policy optimization viewpoint towards policy evaluation for robust Markov decision process with $\mathrm{s}$-rectangular ambiguity sets.

Accelerated stochastic approximation with state-dependent noise

no code implementations4 Jul 2023 Sasila Ilandarideva, Anatoli Juditsky, Guanghui Lan, Tianjiao Li

However, to the best of our knowledge, none of the existing stochastic approximation algorithms for solving this class of problems attain optimality in terms of the dependence on accuracy, problem parameters, and mini-batch size.

Numerical Methods for Convex Multistage Stochastic Optimization

no code implementations28 Mar 2023 Guanghui Lan, Alexander Shapiro

Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP).

Stochastic Optimization Vocal Bursts Type Prediction

Policy Mirror Descent Inherently Explores Action Space

no code implementations8 Mar 2023 Yan Li, Guanghui Lan

SPMD with the second evaluation operator, namely truncated on-policy Monte Carlo (TOMC), attains an $\tilde{\mathcal{O}}(\mathcal{H}_{\mathcal{D}}/\epsilon^2)$ sample complexity, where $\mathcal{H}_{\mathcal{D}}$ mildly depends on the effective horizon and the size of the action space with properly chosen Bregman divergence (e. g., Tsallis divergence).

Efficient Exploration General Reinforcement Learning +1

Policy Optimization over General State and Action Spaces

no code implementations30 Nov 2022 Guanghui Lan

We then define proper notions of the approximation errors for policy evaluation and investigate their impact on the convergence of these methods applied to general-state RL problems with either finite-action or continuous-action spaces.

Reinforcement Learning (RL)

Functional Constrained Optimization for Risk Aversion and Sparsity Control

no code implementations11 Oct 2022 Yi Cheng, Guanghui Lan, H. Edwin Romeijn

The DNCG is the first single-loop projection-free method, with iteration complexity bounded by $\mathcal{O}\big(1/\epsilon^4\big)$ for computing a so-called $\epsilon$-Wolfe point.

Portfolio Optimization

First-order Policy Optimization for Robust Markov Decision Process

no code implementations21 Sep 2022 Yan Li, Guanghui Lan, Tuo Zhao

We consider the problem of solving robust Markov decision process (MDP), which involves a set of discounted, finite state, finite action space MDPs with uncertain transition kernels.

Stochastic first-order methods for average-reward Markov decision processes

no code implementations11 May 2022 Tianjiao Li, Feiyang Wu, Guanghui Lan

We study the problem of average-reward Markov decision processes (AMDPs) and develop novel first-order methods with strong theoretical guarantees for both policy evaluation and optimization.

Policy Gradient Methods

Optimal Methods for Convex Risk Averse Distributed Optimization

no code implementations10 Mar 2022 Guanghui Lan, Zhe Zhang

Specifically, the DRAO method achieves the optimal communication complexity by assuming a certain saddle point subproblem can be easily solved in the server node.

Distributed Optimization

Data-Driven Minimax Optimization with Expectation Constraints

no code implementations16 Feb 2022 Shuoguang Yang, Xudong Li, Guanghui Lan

We propose a class of efficient primal-dual algorithms to tackle the minimax expectation-constrained problem, and show that our algorithms converge at the optimal rate of $\mathcal{O}(\frac{1}{\sqrt{N}})$.

Homotopic Policy Mirror Descent: Policy Convergence, Implicit Regularization, and Improved Sample Complexity

no code implementations24 Jan 2022 Yan Li, Guanghui Lan, Tuo Zhao

We first establish the global linear convergence of HPMD instantiated with Kullback-Leibler divergence, for both the optimality gap, and a weighted distance to the set of optimal policies.

Policy Gradient Methods

Block Policy Mirror Descent

no code implementations15 Jan 2022 Guanghui Lan, Yan Li, Tuo Zhao

Despite the nonconvex nature of the problem and a partial update rule, we provide a unified analysis for several sampling schemes, and show that BPMD achieves fast linear convergence to the global optimality.

reinforcement-learning Reinforcement Learning (RL)

Accelerated and instance-optimal policy evaluation with linear function approximation

no code implementations24 Dec 2021 Tianjiao Li, Guanghui Lan, Ashwin Pananjady

To remedy this issue, we develop an accelerated, variance-reduced fast temporal difference algorithm (VRFTD) that simultaneously matches both lower bounds and attains a strong notion of instance-optimality.

Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process

no code implementations20 Oct 2021 Tianjiao Li, Ziwei Guan, Shaofeng Zou, Tengyu Xu, Yingbin Liang, Guanghui Lan

Despite the challenge of the nonconcave objective subject to nonconcave constraints, the proposed approach is shown to converge to the global optimum with a complexity of $\tilde{\mathcal O}(1/\epsilon)$ in terms of the optimality gap and the constraint violation, which improves the complexity of the existing primal-dual approach by a factor of $\mathcal O(1/\epsilon)$ \citep{ding2020natural, paternain2019constrained}.

Frequency-aware SGD for Efficient Embedding Learning with Provable Benefits

no code implementations ICLR 2022 Yan Li, Dhruv Choudhary, Xiaohan Wei, Baichuan Yuan, Bhargav Bhushanam, Tuo Zhao, Guanghui Lan

We show that incorporating frequency information of tokens in the embedding learning problems leads to provably efficient algorithms, and demonstrate that common adaptive algorithms implicitly exploit the frequency information to a large extent.

Language Modelling Recommendation Systems

Policy Mirror Descent for Reinforcement Learning: Linear Convergence, New Sampling Complexity, and Generalized Problem Classes

no code implementations30 Jan 2021 Guanghui Lan

We further show that the complexity for computing the gradients of these regularizers, if necessary, can be bounded by ${\cal O}\{(\log_\gamma \epsilon) [(1-\gamma)L/\mu]^{1/2}\log (1/\epsilon)\}$ (resp., ${\cal O} \{(\log_\gamma \epsilon ) (L/\epsilon)^{1/2}\}$)for problems with strongly (resp., general) convex regularizers.

Reinforcement Learning (RL)

Optimal Algorithms for Convex Nested Stochastic Composite Optimization

no code implementations19 Nov 2020 Zhe Zhang, Guanghui Lan

All these complexity results seem to be new in the literature and they indicate that the convex NSCO problem has the same order of oracle complexity as those without the nested composition in all but the strongly convex and outer-non-smooth problem.

Stochastic Optimization

Simple and optimal methods for stochastic variational inequalities, II: Markovian noise and policy evaluation in reinforcement learning

no code implementations15 Nov 2020 Georgios Kotsalis, Guanghui Lan, Tianjiao Li

This brings us to the fast TD (FTD) algorithm which combines elements of CTD and the stochastic operator extrapolation method of the companion paper.

CRPO: A New Approach for Safe Reinforcement Learning with Convergence Guarantee

no code implementations11 Nov 2020 Tengyu Xu, Yingbin Liang, Guanghui Lan

To demonstrate the theoretical performance of CRPO, we adopt natural policy gradient (NPG) for each policy update step and show that CRPO achieves an $\mathcal{O}(1/\sqrt{T})$ convergence rate to the global optimal policy in the constrained policy set and an $\mathcal{O}(1/\sqrt{T})$ error bound on constraint satisfaction.

reinforcement-learning Reinforcement Learning (RL) +1

Simple and optimal methods for stochastic variational inequalities, I: operator extrapolation

no code implementations5 Nov 2020 Georgios Kotsalis, Guanghui Lan, Tianjiao Li

In this paper we first present a novel operator extrapolation (OE) method for solving deterministic variational inequality (VI) problems.

A Feasible Level Proximal Point Method for Nonconvex Sparse Constrained Optimization

no code implementations NeurIPS 2020 Digvijay Boob, Qi Deng, Guanghui Lan, Yilin Wang

We also establish new convergence complexities to achieve an approximate KKT solution when the objective can be smooth/nonsmooth, deterministic/stochastic and convex/nonconvex with complexity that is on a par with gradient descent for unconstrained optimization problems in respective cases.

A Primal Approach to Constrained Policy Optimization: Global Optimality and Finite-Time Analysis

no code implementations28 Sep 2020 Tengyu Xu, Yingbin Liang, Guanghui Lan

To demonstrate the theoretical performance of CRPO, we adopt natural policy gradient (NPG) for each policy update step and show that CRPO achieves an $\mathcal{O}(1/\sqrt{T})$ convergence rate to the global optimal policy in the constrained policy set and an $\mathcal{O}(1/\sqrt{T})$ error bound on constraint satisfaction.

Safe Reinforcement Learning

Conditional Gradient Methods for Convex Optimization with General Affine and Nonlinear Constraints

no code implementations30 Jun 2020 Guanghui Lan, Edwin Romeijn, Zhiqiang Zhou

Conditional gradient methods have attracted much attention in both machine learning and optimization communities recently.

A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems

no code implementations3 Jun 2020 Zi Xu, Huiling Zhang, Yang Xu, Guanghui Lan

Moreover, its gradient complexity to obtain an $\varepsilon$-stationary point of the objective function is bounded by $\mathcal{O}\left( \varepsilon ^{-2} \right)$ (resp., $\mathcal{O}\left( \varepsilon ^{-4} \right)$) under the strongly convex-nonconcave (resp., convex-nonconcave) setting.

Complexity of Stochastic Dual Dynamic Programming

no code implementations16 Dec 2019 Guanghui Lan

We then refine these basic tools and establish the iteration complexity for both deterministic and stochastic dual dynamic programming methods for solving more general multi-stage stochastic optimization problems under the standard stage-wise independence assumption.

Decision Making Stochastic Optimization

Stochastic First-order Methods for Convex and Nonconvex Functional Constrained Optimization

no code implementations7 Aug 2019 Digvijay Boob, Qi Deng, Guanghui Lan

For large-scale and stochastic problems, we present a more practical proximal point method in which the approximate solutions of the subproblems are computed by the aforementioned ConEx method.

BIG-bench Machine Learning

GLAD: Learning Sparse Graph Recovery

1 code implementation ICLR 2020 Harsh Shrivastava, Xinshi Chen, Binghong Chen, Guanghui Lan, Srinvas Aluru, Han Liu, Le Song

Recently, there is a surge of interest to learn algorithms directly based on data, and in this case, learn to map empirical covariance to the sparse precision matrix.

Inductive Bias

A unified variance-reduced accelerated gradient method for convex optimization

no code implementations NeurIPS 2019 Guanghui Lan, Zhize Li, Yi Zhou

Moreover, Varag is the first accelerated randomized incremental gradient method that benefits from the strong convexity of the data-fidelity term to achieve the optimal linear convergence.

Cubic Regularization with Momentum for Nonconvex Optimization

no code implementations9 Oct 2018 Zhe Wang, Yi Zhou, Yingbin Liang, Guanghui Lan

However, such a successful acceleration technique has not yet been proposed for second-order algorithms in nonconvex optimization. In this paper, we apply the momentum scheme to cubic regularized (CR) Newton's method and explore the potential for acceleration.

Optimal Adaptive and Accelerated Stochastic Gradient Descent

1 code implementation1 Oct 2018 Qi Deng, Yi Cheng, Guanghui Lan

More specifically, we show that diagonal scaling, initially designed to improve vanilla stochastic gradient, can be incorporated into accelerated stochastic gradient descent to achieve the optimal rate of convergence for smooth stochastic optimization.

BIG-bench Machine Learning Stochastic Optimization

Complexity of Training ReLU Neural Network

no code implementations27 Sep 2018 Digvijay Boob, Santanu S. Dey, Guanghui Lan

In this paper, we explore some basic questions on the complexity of training neural networks with ReLU activation function.

Asynchronous decentralized accelerated stochastic gradient descent

no code implementations24 Sep 2018 Guanghui Lan, Yi Zhou

In this work, we introduce an asynchronous decentralized accelerated stochastic gradient descent type of method for decentralized stochastic optimization, considering communication and synchronization are the major bottlenecks.

Stochastic Optimization

A Note on Inexact Condition for Cubic Regularized Newton's Method

no code implementations22 Aug 2018 Zhe Wang, Yi Zhou, Yingbin Liang, Guanghui Lan

This note considers the inexact cubic-regularized Newton's method (CR), which has been shown in \cite{Cartis2011a} to achieve the same order-level convergence rate to a secondary stationary point as the exact CR \citep{Nesterov2006}.

Stochastic Variance-Reduced Cubic Regularization for Nonconvex Optimization

no code implementations20 Feb 2018 Zhe Wang, Yi Zhou, Yingbin Liang, Guanghui Lan

Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization.

Theoretical properties of the global optimizer of two-layer Neural Network

no code implementations ICLR 2018 Digvijay Boob, Guanghui Lan

We essentially show that these non-singular hidden layer matrix satisfy a ``"good" property for these big class of activation functions.

Vocal Bursts Valence Prediction

Random gradient extrapolation for distributed and stochastic optimization

no code implementations15 Nov 2017 Guanghui Lan, Yi Zhou

Furthermore, we demonstrate that for stochastic finite-sum optimization problems, RGEM maintains the optimal ${\cal O}(1/\epsilon)$ complexity (up to a certain logarithmic factor) in terms of the number of stochastic gradient computations, but attains an ${\cal O}(\log(1/\epsilon))$ complexity in terms of communication rounds (each round involves only one agent).

Stochastic Optimization

Theoretical properties of the global optimizer of two layer neural network

no code implementations30 Oct 2017 Digvijay Boob, Guanghui Lan

We look at this problem in the setting where the number of parameters is greater than the number of sampled points.

Vocal Bursts Valence Prediction

Dynamic Stochastic Approximation for Multi-stage Stochastic Optimization

no code implementations11 Jul 2017 Guanghui Lan, Zhiqiang Zhou

We show that DSA can achieve an optimal ${\cal O}(1/\epsilon^4)$ rate of convergence in terms of the total number of required scenarios when applied to a three-stage stochastic optimization problem.

Stochastic Optimization

Conditional Accelerated Lazy Stochastic Gradient Descent

no code implementations ICML 2017 Guanghui Lan, Sebastian Pokutta, Yi Zhou, Daniel Zink

In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate $O\left(\frac{1}{\varepsilon^2}\right)$ improving over the projection-free, Online Frank-Wolfe based stochastic gradient descent of Hazan and Kale [2012] with convergence rate $O\left(\frac{1}{\varepsilon^4}\right)$.

Communication-Efficient Algorithms for Decentralized and Stochastic Optimization

no code implementations14 Jan 2017 Guanghui Lan, Soomin Lee, Yi Zhou

Our major contribution is to present a new class of decentralized primal-dual type algorithms, namely the decentralized communication sliding (DCS) methods, which can skip the inter-node communications while agents solve the primal subproblems iteratively through linearizations of their local objective functions.

Stochastic Optimization

Algorithms for stochastic optimization with functional or expectation constraints

no code implementations13 Apr 2016 Guanghui Lan, Zhiqiang Zhou

We then present a variant of CSA, namely the cooperative stochastic parameter approximation (CSPA) algorithm, to deal with the situation when the constraint is defined over problem parameters and show that it exhibits similar optimal rate of convergence to CSA.

Stochastic Optimization

Generalized Uniformly Optimal Methods for Nonlinear Programming

no code implementations29 Aug 2015 Saeed Ghadimi, Guanghui Lan, Hongchao Zhang

In a similar vein, we show that some well-studied techniques for nonlinear programming, e. g., Quasi-Newton iteration, can be embedded into optimal convex optimization algorithms to possibly further enhance their numerical performance.

An optimal randomized incremental gradient method

no code implementations8 Jul 2015 Guanghui Lan, Yi Zhou

We first introduce a deterministic primal-dual gradient (PDG) method that can achieve the optimal black-box iteration complexity for solving these composite optimization problems using a primal-dual termination criterion.

Gradient Sliding for Composite Optimization

1 code implementation4 Jun 2014 Guanghui Lan

We consider in this paper a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term.

Accelerated Gradient Methods for Nonconvex Nonlinear and Stochastic Programming

1 code implementation14 Oct 2013 Saeed Ghadimi, Guanghui Lan

We demonstrate that by properly specifying the stepsize policy, the AG method exhibits the best known rate of convergence for solving general nonconvex smooth optimization problems by using first-order information, similarly to the gradient descent method.

Optimization and Control

Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming

no code implementations22 Sep 2013 Saeed Ghadimi, Guanghui Lan

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.

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