A Contextual Combinatorial Bandit Approach to Negotiation

Abstract#

We present a novel contextual combinatorial bandit approach for automated negotiation in multi-agent settings. Our method addresses the challenge of learning effective negotiation strategies when the opponent’s behavior and preferences are unknown.

Introduction#

Automated negotiation is a fundamental problem in multi-agent systems, with applications ranging from resource allocation to market trading. Traditional approaches often assume perfect information about opponent preferences, which is unrealistic in many real-world scenarios.

Problem Formulation#

We formalize the negotiation problem as a contextual combinatorial bandit where:

• Actions: Negotiation offers (combinations of items/terms)
• Context: Current negotiation state and opponent behavior history
• Rewards: Negotiation outcomes (acceptance/rejection and utility)

Method#

Contextual Combinatorial Bandit Framework#

Our approach extends the combinatorial bandit setting to incorporate:

1. Context-aware Policy: Learns to adapt strategies based on negotiation context
2. Combinatorial Action Space: Handles complex offer structures
3. Online Learning: Adapts to opponent behavior during negotiation

Algorithm Design#

The core algorithm follows these steps:

1. Context Extraction: Extract relevant features from current negotiation state
2. Offer Generation: Use upper confidence bounds to select promising offers
3. Response Learning: Update model based on opponent’s response
4. Strategy Adaptation: Refine negotiation strategy over time

Theoretical Analysis#

We provide regret bounds for our algorithm, showing:

• Sublinear Regret: O(√T log T) regret with respect to optimal strategy
• Context Adaptation: Improved bounds when context is informative
• Combinatorial Efficiency: Polynomial dependence on action space complexity

Experimental Results#

Simulated Environments#

• Bilateral Negotiation: Consistent improvements over baseline strategies
• Multi-issue Negotiation: Effective handling of complex negotiation spaces
• Opponent Adaptation: Quick adaptation to different opponent types

Real-world Application#

• Online Marketplace: Improved success rates in automated trading
• Resource Allocation: Better outcomes in distributed resource sharing

Key Contributions#

1. Novel Formulation: First to cast negotiation as contextual combinatorial bandit
2. Theoretical Guarantees: Rigorous analysis with regret bounds
3. Practical Algorithm: Efficient implementation with strong empirical performance
4. Broad Applicability: Demonstrated effectiveness across multiple domains

Related Work#

Our work builds upon:

• Combinatorial bandits literature
• Game-theoretic approaches to negotiation
• Online learning in multi-agent systems

Conclusion#

We have presented a principled approach to automated negotiation using contextual combinatorial bandits. Our method provides both theoretical guarantees and practical performance improvements, opening new directions for research in multi-agent learning.

Citation#

@inproceedings{li2024negotiation,
  title={A Contextual Combinatorial Bandit Approach to Negotiation},
  author={Li, Yexin and Mu, Zhancun and Qi, Siyuan},
  booktitle={International Conference on Machine Learning},
  year={2024}
}