SOC Reading Group

Speaker: Feng-Yi Liao [Slides]

Supplemental Material: 

• Gradient Descent Only Converges to Minimizers 

• First-order Methods Almost Always Avoid Saddle Points 

Speaker: Jiachen Qian [Slides]

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Speaker: Xu Shang [Slides]

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• Optimal filtering

Speaker: Yuto Watanabe [Slides]

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• Deterministic Nonsmooth Nonconvex Optimization

• A gradient sampling method with complexity guarantees for Lipschitz functions in high and low dimensions

Speaker: Feng-Yi Liao [Slides]

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• Convex Analysis and Minimization Algorithms I

• Subgradient Regularization: A Descent-Oriented Subgradient Method for Nonsmooth Optimization

Speaker: Pranav Reddy [Slides]

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• Steepest Descent Method with Random Step Lengths

• Acceleration by Random Stepsizes: Hedging, Equalization, and the Arcsine Stepsize Schedule

Speaker: Jiachen Qian [Slides]

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• A Tutorial on the Non-Asymptotic Theory of System Identification

Speaker: Xu Shang [Slides]

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• ChooseWisely: Data-Enabled Predictive Control for Nonlinear Systems Using Online Data Selection

• A Global Geometric Frameworkfor Nonlinear DimensionalityReduction

Speaker: Yuto Watanabe [Slides]

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• Notions of Stationarity in Nonsmooth Optimization: A Guided Tour of Various Constructions of Subdifferential for Nonsmooth Functions

Speaker: Rich Pai [Slides]

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•  The Power of Predictions in Online Control.

Speaker: Feng-Yi Liao [Slides]

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• Algebraic characterization of equivalence between optimization algorithms

Speaker: Pranav Reddy  [Slides]

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• On the local stability of semidefinite relaxations

Speaker: Jiachen Qian  [Slides]

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• SLIP: Learning to Predict in Unknown Dynamical Systems with Long-Term Memory

• Supplementary Material

Speaker: Xu Shang  [Slides]

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Speaker: Yuto Watanabe  [Slides]

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• Linear-quadratic regulator and H∞ analysis problems via covariance representations and duality

• Simple Covariance Approach to H∞ Analysis

Speaker: Rich Pai  [Slides]

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• Dynamic regret of online LQR with predictions

• Online (stochastic) LQR

Speaker: Feng-Yi Liao [Slides]

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• Dual Method

• The Proximal Bundle Algorithm Under a Frank-Wolfe Perspective:  an Improved Complexity Analysis

Speaker: Pranav Reddy [Slides]

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• Notes on Distributed Optimization

Speaker: Xu Shang  [Slides]

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• Disturbance attenuation in LTI plants with finite horizon: Optimality of nonlinear controllers

Speaker: Chendi Qv  [Slides]

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• Approximation Methods for Bilevel Programming

• Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework

Speaker: Jiachen Qian  [Slides]

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• Online Learning of the Kalman Filter With Logarithmic Regret

• Regret-Optimal Estimation and Control

Speaker: Yuto Watanabe  [Slides]

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• Complexity of Derivative-Free Policy Optimization for Structured H∞ Control

• Global Convergence of Direct Policy Search for State-Feedback H1 Robust Control: A Revisit of Nonsmooth Synthesis with Goldstein Subdifferential

Speaker: Rich Pai  [Slides]

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• Non-stationary Online Learning and Non-stochastic Control

Speaker: Feng-Yi Liao  [Slides]

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• A simple nearly optimal restart scheme for speeding up first-order methods

Speaker: Pranav Reddy [Slides]

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• Notes on Distributed Optimization

Speaker: Rich Pai [Slides]

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• Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints

Speaker: Feng-Yi Liao [Slides]

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• Universal gradient methods for convex optimization problems

Speaker: Xu Shang[Slides]

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• Linear tracking MPC for nonlinear systems Part II: The data-driven case 

Speaker: Rich Pai [Slides]

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• On the Stability and Convergence of Robust Adversarial Reinforcement Learning: A Case Study on Linear Quadratic Systems

• Policy Optimization Provably Converges to Nash Equilibria in Zero-Sum Linear Quadratic Games

Speaker: Feng-Yi Liao [Slides]

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• Complementarity and nondegeneracy in semidefinite programming

• Strict Complementarity always holds in Linear Programs

Speaker: Pranav Reddy [Slides]

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• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming

Speaker: Xu Shang [Slides]

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• Model Predictive Control: Theory, Computation and Design

• Examples of Zero Robustness in Constrained Model Predictive Control

Speaker: Rich Pai [Slides]

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• A Direct Approach to Robustness Optimization

Speaker: Feng-Yi Liao [Slides]

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• On the tightness of SDP relaxations of QCQPs

Speaker: Pranav Reddy [Slides]

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• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming

• A dual approach to solving nonlinear programming problems by unconstrained optimization

Speaker: Liwei Jiang

Abstract: Nonsmooth optimization problems appear throughout machine learning and signal processing. Standard gradient methods in nonsmooth optimization are often described as “slow” since the well-known “lower-complexity bounds” suggest they converge at best sublinearly. In this talk, I will introduce a gradient method that (locally) exponentially improves upon such lower bounds. The method is “parameter-free” and converges nearly linearly on “typical” optimization problems. The key insight is that “typical” nonsmooth functions are not pathological but are instead “partially smooth” in algorithmically useful ways.

Bio: Liwei Jiang is a fifth-year Ph.D. candidate in the School of Operations Research and Information Engineering (ORIE) at Cornell University. Previously, he obtained B.S. in Mathematics and Statistics from Nanjing University in 2019 and M.S. in Operations Research from Cornell in 2022. His fields of interest are optimization, data science, and machine learning. His research focuses on designing, analyzing, and accelerating optimization algorithms for modern estimation and learning problems. Liwei is a recipient of the Hsien Wu and Daisy Yen Wu Scholarship and a two-time recipient of Cornell ORIE's Teaching Assistant of the Year award.

Speaker: Yiheng  Lin 

Abstract: In this talk, I will introduce our work on online policy optimization under time-varying dynamics and costs with possibly unknown dynamical models. We study a setting where the online agent seeks to minimize the total cost incurred over a finite horizon by optimizing the parameters for a given policy class. We propose the Gradient-based Adaptive Policy Selection (GAPS) algorithm that achieves the optimal policy regret and is efficient to implement. The key component of our theoretical analysis is establishing the connections between GAPS for online policy optimization and online gradient descent (OGD) for classic online optimization problem, which allow us to ‘transfer’ existing regret guarantees for OGD to GAPS. Further, I will present a meta-framework that can combine an online policy optimization algorithm like GAPS with an online model estimator to address the challenge of unknown nonlinear dynamical models. Compared with many prior works that study online control in unknown linear dynamical systems, our work provides a critical insight that learning the true dynamical model globally is unnecessary. Instead, the online model estimator only needs to predict well on the actual trajectory visited by the controller, which is a tractable goal for general nonlinear dynamical systems.  

Bio: Yiheng Lin is a fourth-year Ph.D. candidate in the Department of Computing and Mathematical Sciences at California Institute of Technology. He is co-advised by Prof. Adam Wierman and Prof. Yisong Yue. Yiheng was named an Amazon/Caltech AI4Science Fellow in 2023, a PIMCO Graduate Fellow in Data Science in 2022, and a Kortschak Scholar in 2020. His research interests include online learning, control, and reinforcement learning.

Speaker: 

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• TBD

Discussion Leader:  Xu Shang, [Slides]

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• Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition

Discussion Leader:  Xu Shang, 

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• TBD

Discussion Leader:  Rich Pai, [Slides]

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• Semidefinite Programming Duality and Linear Time-invariant Systems

Discussion Leader: Feng-Yi Liao, [Slides]

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• Nonsmooth optimization using Taylor-like models: error bounds, convergence, and termination criteria

Discussion Leader: Pranav Reddy, [Slides]

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•  Exact Worst-case Performance of First-order Methods for Composite Convex Optimization

• Smooth Strongly Convex Interpolation and Exact Worst-case Performance of First-order Methods

Discussion Leader: Xu Shang, [Slides]

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• Modeling Nonlinear Control Systems via Koopman Control Family: Universal Forms and Subspace Invariance Proximity

Discussion Leader: Hesam Mojtahedi, [Slides]

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• Nonlinear Control (Advanced topics in stability)

Discussion Leader: Rich Pai, [Slides]

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• Distributionally Robust Linear Quadratic Control

Discussion Leader: Pranav Reddy, [Slides]

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• Smooth convex Interpolation and first-order methods

• Convex Analysis

Discussion Leader: Xu Shang, [Slides]

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• On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator

• Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control

• A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

Discussion Leader: Hesam Mojtahedi, [Slides]

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• An introduction to Optimization on smooth manifolds

• Optimization Algorithms on Matrix Manifolds

Discussion Leader: Rich Pai, [Slides]

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• The effect of smooth parametrizations on nonconvex optimization landscapes

Discussion Leader: Feng-Yi Liao, [Slides]

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• Convex analysis and Nonsmooth optimization

Discussion Leader: Xu Shang, [Slides]

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• The Koopman Operator in System and Control

• On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator

• Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control

Discussion Leader: Hesam Mojtahedi, [Slides]

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• An introduction to Optimization on smooth manifolds

Discussion Leader: Rich Pai, [Slides]

Supplemental Material: 

• Deterministic Nonsmooth Nonconvex Optimization

• Complexity of Finding Stationary Points of Nonsmooth Nonconvex Functions