Regret Minimization-based Learning Algorithm

A Regret Minimization-based Learning Algorithm is a learning algorithm that can be implemented by a regret minimization system (to solve regret minimization tasks to enable strategy optimization through regret tracking and iterative updating (to minimize cumulative regret over sequential decisions).

• AKA: Regret-Based Learning Algorithm, No-Regret Learning Algorithm.
• Context:
  • Task Input: decision space, reward function
    • Optional Input: initial strategy, learning parameters
  • Task Output: optimized strategy, regret bounds
  • Task Performance Measure: average regret, convergence speed, sample complexity
  • ...
  • It can typically compute Regret Value through reward difference calculation.
  • It can typically update Strategy Profile through regret-based adjustment.
  • It can typically maintain Action Distribution through probability updating.
  • It can typically handle Online Learning through incremental adaptation.
  • It can typically bound Performance Loss through regret minimization.
  • ...
  • It can often support Multi-Armed Bandit through exploration-exploitation balancing.
  • It can often process Sequential Game through history-dependent learning.
  • It can often handle Adversarial Environment through robust optimization.
  • It can often manage Partial Feedback through bandit feedback.
  • ...
  • It can range from being a Simple Regret Algorithm to being a Complex Regret Algorithm, depending on its decision space complexity.
  • It can range from being a Deterministic Algorithm to being a Stochastic Algorithm, depending on its update mechanism.
  • ...
  • It can integrate with Function Approximator for value estimation.
  • It can support Parallel Computing for computational efficiency.
  • It can connect to Decision System for strategy deployment.
  • ...
• Examples:
  • Core Algorithms, such as:
    • Basic Regrets, such as:
      • Follow The Leader for full information setting.
      • Follow The Regularized Leader for stability improvement.
    • Advanced Regrets, such as:
      • Counterfactual Regret Minimization (CFR) Algorithm for imperfect information games.
      • Hedge Algorithm for expert advice setting.
  • Application Types, such as:
    • Online Learnings, such as:
      • Portfolio Selection Algorithm for investment optimization.
      • Ad Placement Algorithm for advertising strategy.
    • Game Theorys, such as:
      • Equilibrium Computing Algorithm for nash equilibrium finding.
      • Strategy Learning Algorithm for optimal play discovery.
  • ...
• Counter-Examples:
  • Gradient Descent Algorithm, which lacks explicit regret tracking.
  • Value Iteration Algorithm, which lacks online learning capability.
  • Evolutionary Algorithm, which lacks regret-based updating.
• See: Learning Algorithm, Online Learning, Strategy Optimization, Regret Theory, Decision Theory, Game Theory.

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