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This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity…
DPO is an effective preference optimization algorithm. However, the DPO-tuned models tend to overfit on the dispreferred samples, manifested as overly long generations lacking diversity. While recent regularization approaches have…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
We focus on finding sparse and least-$\ell_1$-norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, nevertheless recent versions of Newton method for under-determined…
Bayesian Optimization (BO) is a sample-efficient optimization algorithm widely employed across various applications. In some challenging BO tasks, input uncertainty arises due to the inevitable randomness in the optimization process, such…
Safe reinforcement learning aims to learn the optimal policy while satisfying safety constraints, which is essential in real-world applications. However, current algorithms still struggle for efficient policy updates with hard constraint…
This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a…
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set…
Recent advances in deep learning have enabled optimization of deep reactive policies (DRPs) for continuous MDP planning by encoding a parametric policy as a deep neural network and exploiting automatic differentiation in an end-to-end…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and…
In this work, we treat the problem of multi-task submodular optimization from the perspective of local distributional robustness within the neighborhood of a reference distribution which assigns an importance score to each task. We…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
We present PANOC, a new algorithm for solving optimal control problems arising in nonlinear model predictive control (NMPC). A usual approach to this type of problems is sequential quadratic programming (SQP), which requires the solution of…
Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying…
Submodular maximization arises in many applications, and has attracted a lot of research attentions from various areas such as artificial intelligence, finance and operations research. Previous studies mainly consider only one kind of…