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Adaptive State-Dependent Diffusion for Derivative-Free Optimization
Optimization and Control · Submitted 8 Feb 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We prove global convergence in probability with algebraic rate and give the quantitative results in numerical examples.
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The abstract, sentence by sentence
This paper develops and analyzes a stochastic derivative-free optimization strategy. A key feature is the state-dependent adaptive variance. We prove global convergence in probability with algebraic rate and give the quantitative results in numerical examples. A striking fact is that convergence is achieved without explicit information of the gradient and even without comparing different objective function values as in established methods such as the simplex method and simulated annealing. It can otherwise be compared to annealing with state-dependent temperature.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This paper develops and analyzes a stochastic derivative-free optimization strategy. | contribution 1.00 | 0.94 | 0.08 | asserted 1.00 |
| s1 | A key feature is the state-dependent adaptive variance. | method 0.69 | 0.75 | 0.06 | asserted 1.00 |
| s2 | We prove global convergence in probability with algebraic rate and give the quantitative results in numerical examples. | result 0.83 | 0.96 | 0.71 | asserted 1.00 |
| s3 | A striking fact is that convergence is achieved without explicit information of the gradient and even without comparing different objective function values as in established methods such as the simplex method and simulated annealing. | result 0.68 | 0.85 | 0.25 | asserted 1.00 |
| s4 | It can otherwise be compared to annealing with state-dependent temperature. | interpretation 0.98 | 0.39 | 0.06 | asserted 0.57 |
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The paper
Original abstract
This paper develops and analyzes a stochastic derivative-free optimization strategy. A key feature is the state-dependent adaptive variance. We prove global convergence in probability with algebraic rate and give the quantitative results in numerical examples. A striking fact is that convergence is achieved without explicit information of the gradient and even without comparing different objective function values as in established methods such as the simplex method and simulated annealing. It can otherwise be compared to annealing with state-dependent temperature.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Cites it as support 1 paper
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Second, and conversely, against the common wisdom that derivative-free optimization heuristics search the domain mainly by random exploration and therefore ought to be inefficient, we provide evidence that such heuristics in fact work successfully in finding benign optima [ref] , precisely because they are suitable stochastic relaxations of gradient-based methods.
Gradient is All You Need? How Consensus-Based Optimization can be Interpreted as a Stochastic Relaxation of Gradient Descent · Introduction · 1.00
What it cites · 13 sentences without a confident label
Builds on 1 paper
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In this paper, we improve the result in [ref] by considering a derivative-free version of the algorithm.
An Algebraically Converging Stochastic Gradient Descent Algorithm for Global Optimization · Introduction · 0.99
Uses the method or tool of 1 paper
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There are abnormal cases where the estimate [ref] would require very slow decay of $(t)$, and for a rigorous convergence result, we adopt the same strategy, which we used in [ref] , of basing the hyperparameter estimates on extra sampling.
An Algebraically Converging Stochastic Gradient Descent Algorithm for Global Optimization · Estimating optimal objective function value · 0.86
Compares with 1 paper
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We also point out in <Ref> the close connection as well as main differences of scheme [ref] to our previous work of [ref] .
An Algebraically Converging Stochastic Gradient Descent Algorithm for Global Optimization · Introduction · 0.97
Cites as background 3 papers
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The basic concept of adding a stochastic term in the optimization algorithm with the variance of that term being state-dependent was already introduced in [ref] .
An Algebraically Converging Stochastic Gradient Descent Algorithm for Global Optimization · Revisiting the AdaVar Stochastic Gradient Descent Algorithm in · 0.95
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Different stochastic mechanisms have been developed in the literature based on time-dependent diffusion [ref] .
Consensus-Based Optimization Methods Converge Globally · Introduction · 1.00
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While it is impossible to have an xhaustive list of successive methods in this direction, let us mention, as examples, the Nelder–Mead (NM) method [ref] , which performs a direct search in the parameter space using function value comparison, the genetic algorithm (GA) [ref] , simulated annealing (SA) [ref] , the particle swarm optimization (PSO) method [ref] , and the consensus-based optimization method [ref] .
Trends in Consensus-based optimization · Introduction · 0.94
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