Related papers: The (1+1)-ES Reliably Overcomes Saddle Points
We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…
A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from…
In centralized settings, it is well known that stochastic gradient descent (SGD) avoids saddle points and converges to local minima in nonconvex problems. However, similar guarantees are lacking for distributed first-order algorithms. The…
This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…
Gradient descent is a popular algorithm in optimization, and its performance in convex settings is mostly well understood. In non-convex settings, it has been shown that gradient descent is able to escape saddle points asymptotically and…
Evolution strategy (ES) is one of the promising classes of algorithms for black-box continuous optimization. Despite its broad successes in applications, theoretical analysis on the speed of its convergence is limited on convex quadratic…
This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…
Convergence of Extremum Seeking (ES) algorithms has been established in the limit of small gains. Using averaging theory and contraction analysis, we propose a framework for computing explicit bounds on the departure of the ES scheme from…
Recently, in (M. Masoudi, D.K. Salkuyeh, An extension of positive-definite and skew-Hermitian splitting method for preconditioning of generalized saddle point problems, Computers \& Mathematics with Application,…
The mutation process in evolution strategies has been interlinked with the normal distribution since its inception. Many lines of reasoning have been given for this strong dependency, ranging from maximum entropy arguments to the need for…
In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…
We propose an approach to saddle point optimization relying only on oracles that solve minimization problems approximately. We analyze its convergence property on a strongly convex--concave problem and show its linear convergence toward the…
Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…
Optimization algorithms are unlikely to converge to strict saddle points. Proofs to that effect rely on the Center-Stable Manifold Theorem (CSMT), casting algorithms as dynamical systems: $x_{k+1} = g_k(x_k)$. In its standard form, the CSMT…
Real-world reinforcement learning often faces environment drift, but most existing methods rely on static entropy coefficients/target entropy, causing over-exploration during stable periods and under-exploration after drift, and leaving…
The note considers normalized gradient descent (NGD), a natural modification of classical gradient descent (GD) in optimization problems. A serious shortcoming of GD in non-convex problems is that GD may take arbitrarily long to escape from…
An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative (``mutant'') strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper we address the…
We propose an alternating subgradient method with non-constant step sizes for solving convex-concave saddle-point problems associated with general convex-concave functions. We assume that the sequence of our step sizes is not summable but…
Drift analysis aims at translating the expected progress of an evolutionary algorithm (or more generally, a random process) into a probabilistic guarantee on its run time (hitting time). So far, drift arguments have been successfully…
We consider SDEs of the form $dX_t = |f(X_t)|/t^{\gamma} dt+1/t^{\gamma} dB_t$, where $f(x)$ behaves comparably to $|x|^k$ in a neighborhood of the origin, for $k\in [1,\infty)$. We show that there exists a threshold value…