artificial intelligence - In counterfactual regret minimization, why are additions to regret weighted by reach probability? - Computer Science Stack Exchange

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• artificial intelligence - In counterfactual regret minimization, why are additions to regret weighted by reach probability? - Computer Science Stack Exchange

In Counterfactual Regret Minimization, Why Are Additions to Regret Weighted by Reach Probability?

Context

The question explores the reasoning behind weighting additions to regret and strategy in Counterfactual Regret Minimization (CFR) algorithms.

Original Algorithm Lines

25.  rI[a] ← rI[a] + π−i.(vσI→a[a] − vσ[a])
26.  sI[a] ← sI[a] + πi.σt(I,a)

Key Variables

• rI[a]: Accumulated regret for information set I and action a
• sI[a]: Accumulated strategy for information set I and action a
• πi: Probability of reaching game state for learning player
• π−i: Probability of reaching game state for other player

Motivation

The weighting serves two primary purposes:

1. Compute strategy with reasonable runtime
2. Create an upper bound on overall regret that can be minimized

Theoretical Basis

The approach is grounded in the paper "Regret Minimization in Games with Incomplete Information", which proves that overall regret is bounded by cumulative counterfactual regret.

The goal is to approximate a Nash equilibrium strategy by systematically minimizing cumulative counterfactual regret across multiple iterations.

Tags

• artificial-intelligence
• probability-theory
• game-theory

Suggested labels

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