---
title: No-Regret Algorithms
url: https://www.emergentmind.com/topics/no-regret-algorithms
type: topic
---

# No-Regret Algorithms

A no-regret algorithm is an online decision-making procedure that ensures the cumulative cost (or regret) incurred by the learner, as compared to the best possible fixed decision or policy in hindsight, grows sublinearly with time. This property enables the algorithm to asymptotically match the performance of the optimal offline strategy, even under adversarial or nonstationary environments. No-regret algorithms are foundational to online convex optimization, adaptive control, online combinatorial optimization, and repeated games, and are essential to theoretical and practical advances in both AI and economics. They underpin guarantees for learning efficacy, strategic robustness, and the emergence of equilibria in multi-agent systems. 

## 1. Formal Regret Notions and Definitions

No-regret algorithms are defined relative to a regret metric that compares the cumulative reward (

Source: https://www.emergentmind.com/topics/no-regret-algorithms