Safeguarded Learned Convex Optimization
Applications abound in which optimization problems must be repeatedly solved, each time with new (but similar) data. Analytic optimization algorithms can be hand-designed to provably solve these problems in an iterative fashion. On one hand, data-driven algorithms can "learn to optimize" (L2O) with much fewer iterations and similar cost per iteration as general-purpose optimization algorithms. On the other hand, unfortunately, many L2O algorithms lack converge guarantees. To fuse the advantages of these approaches, we present a Safe-L2O framework. Safe-L2O updates incorporate a safeguard to guarantee convergence for convex problems with proximal and/or gradient oracles. The safeguard is simple and computationally cheap to implement, and it is activated only when the data-driven L2O updates would perform poorly or appear to diverge. This yields the numerical benefits of employing machine learning to create rapid L2O algorithms while still guaranteeing convergence. Our numerical examples show convergence of Safe-L2O algorithms, even when the provided data is not from the distribution of training data.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Safeguarded Stochastic Polyak Step Sizes for Non-smooth Optimization: Robust Performance Without Small (Sub)Gradients
The stochastic Polyak step size (SPS) has proven to be a promising choice for stochastic gradient descent (SGD), delivering competitive performance relative to state-of-the-art methods on smooth convex and non-convex opt…
Universal Safeguarded Learned Convex Optimization with Guaranteed Convergence
Many applications require quickly and repeatedly solving a certain type of optimization problem, each time with new (but similar) data. However, state of the art general-purpose optimization methods may converge too slo…
A Simple Guard for Learned Optimizers
If the trend of learned components eventually outperforming their hand-crafted version continues, learned optimizers will eventually outperform hand-crafted optimizers like SGD or Adam. Even if learned optimizers (L2Os) …
Anytime-Feasible First-Order Optimization via Safe Sequential QCQP
This paper presents the Safe Sequential Quadratically Constrained Quadratic Programming (SS-QCQP) algorithm, a first-order method for smooth inequality-constrained nonconvex optimization that guarantees feasibility at ev…
Open-Weight LLM Fine-Tuning Defenses are Susceptible to Simple Attacks
Recent defenses for safeguarding open-weight large language models (LLMs) are intended to prevent adversarial usage. Underlying these defenses is an assumption that new harmful behavior is learned through fine-tuning rat…