---
title: "Strongly Adaptive Online Learning Achieves Uniform Discounted Regret"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2610.39292v1"
permalink: "https://feed.astralor.com/items/itm_af5a398387f7aa280d0dc16d"
published: "2026-10-29T03:41:46.000Z"
score: 53
channel: "ai"
tags: ["Strongly Adaptive Online","Learning Achieves Uniform","Discounted Regret Discounted","While","Discounted","Our","For"]
---

# Strongly Adaptive Online Learning Achieves Uniform Discounted Regret

## 速览

Discounted regret measures the performance of an online learner by assigning exponentially decaying weights to past losses, reflecting the greater importance of recent losses in non-stationary online learning. While pre…

## 关键点

- Discounted regret measures the performance of an online learner by assigning exponentially decaying weights to past losses, reflecting the greater importance of recent losses in non-stationary online learning.
- While previous work obtains uniform discounted regret bounds over a continuous range of discount factors using a specialized meta-algorithm, its results are limited to convex functions.
- In this paper, we demonstrate that strongly adaptive regret bounds can directly imply uniform discounted regret guarantees for convex, strongly convex, and exp-concave loss functions.

## 全文

Discounted regret measures the performance of an online learner by assigning exponentially decaying weights to past losses, reflecting the greater importance of recent losses in non-stationary online learning. While previous work obtains uniform discounted regret bounds over a continuous range of discount factors using a specialized meta-algorithm, its results are limited to convex functions. In this paper, we demonstrate that strongly adaptive regret bounds can directly imply uniform discounted regret guarantees for convex, strongly convex, and exp-concave loss functions. Our key observation is that discounted regret against a fixed comparator admits an exact decomposition into a convex combination of interval regrets. For convex functions, this reduction yields an $O(\sqrt{\log T/(1-λ)})$ discounted regret bound for all discount factors $λ\in(0,1)$, matching the previous rate over a broader range of discount factors. For strongly convex and exp-concave functions, we provide regret bounds of $O\left(\log T\left(1+\log\frac{1}{1-λ}\right)\right)$.

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