Multi-Constraint Optimization for Real-Time Bidding: A Reinforcement Learning Approach

Abstract

Real-time bidding ecosystems demand sophisticated algorithmic frameworks capable of navigating complex multi-objective optimization landscapes while maintaining computational efficiency. This paper presents a comprehensive methodology integrating Lagrangian dual decomposition with policy gradient reinforcement learning for dynamic bid optimization under heterogeneous constraints. Our approach transforms the traditionally discrete auction participation problem into a continuous optimization framework, enabling gradient-based learning while preserving budget and performance constraints. Experimental validation across industrial-scale datasets demonstrates substantial improvements in campaign performance metrics, achieving 34.7% higher conversion rates compared to baseline methods while maintaining strict budget compliance. The proposed framework addresses critical challenges in modern programmatic advertising, including budget pacing, conversion optimization, and real-time decision making under uncertainty. Policy gradient algorithms combined with constraint softening mechanisms enable adaptive bidding strategies that respond dynamically to market conditions and inventory availability. Our contributions extend beyond algorithmic innovation to practical deployment considerations, providing advertising platforms with actionable insights for implementing scalable bid optimization systems.

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