Scholarlink

<p>In this paper, we consider the distributed online optimization problem on a time-varying network, where each agent on the network has its own time-varying objective function and the goal is to minimize the overall loss accumulated. Moreover, we focus on distributed algorithms which do not use gradient information and projection operators to improve the applicability and computational efficiency. By introducing the deterministic differences and the randomized differences to substitute the gradient information of the objective functions and removing the projection operator in the traditional algorithms, we design two kinds of gradient-free distributed online optimization algorithms without projection step, which can economize considerable computational resources as well as has less limitations on the applicability. We prove that both of two algorithms achieves consensus of the estimates and regrets of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11768_2025_242_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\(O\left( \log (T)\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mfenced close=")" open="("> <mo>log</mo> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mfenced> </mrow> </math></EquationSource> </InlineEquation> for local strongly convex objective, respectively. Finally, a simulation example is provided to verify the theoretical results.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Gradient-free distributed online optimization in networks

  • 期刊论文

  • 发表日期：

    2025年2月11日

查看全文
  • Yuhang Liu,
  • Wenxiao Zhao,
  • Nan Zhang,
  • Dongdong Lv,
  • Shuai Zhang

摘要

In this paper, we consider the distributed online optimization problem on a time-varying network, where each agent on the network has its own time-varying objective function and the goal is to minimize the overall loss accumulated. Moreover, we focus on distributed algorithms which do not use gradient information and projection operators to improve the applicability and computational efficiency. By introducing the deterministic differences and the randomized differences to substitute the gradient information of the objective functions and removing the projection operator in the traditional algorithms, we design two kinds of gradient-free distributed online optimization algorithms without projection step, which can economize considerable computational resources as well as has less limitations on the applicability. We prove that both of two algorithms achieves consensus of the estimates and regrets of \(O\left( \log (T)\right) \) O log ( T ) for local strongly convex objective, respectively. Finally, a simulation example is provided to verify the theoretical results.