Deployment-Time Optimization of AI: Robustness, Compression, Evaluation, Inference, and Adaptive Environments

What changes when a trained model leaves the training cluster and becomes a deployed AI system? The optimization problem changes with it. Threat models, serving budgets, evaluation protocols, users, tools, and feedback loops now shape what can be optimized—and what must be guaranteed, measured, compressed, routed, or constrained.

This graduate-level text develops a mathematical account of those deployment-induced decisions. It begins with robust value functions, minimax structure, adversarial training dynamics, distributionally robust optimization, robust generalization, and certification. It then turns to the system-level problems that dominate modern foundation-model deployment: curvature-aware compression and rate–distortion tradeoffs; evaluation as a problem of estimands, information, and adversarial search; threat models and reachability for language models and agents; and inference-time optimization through sampling, verification, speculative decoding, routing, cascades, and cache decisions. The final chapters study deployment games in which resources can improve quality while also expanding adversarial exposure, responsive environments in which users change the data distribution, and lifecycle questions involving continual learning, machine unlearning, privacy, and feedback into the next training run.

Rather than serving as an adversarial-ML catalog or an LLM serving handbook, Deployment-Time Optimization for AI Systems focuses on durable mathematical objects: value functions, feasible sets, rate–distortion frontiers, estimands, reachability sets, and shadow prices. It is designed for graduate students, researchers, and engineers who want to reason rigorously about how foundation models become deployed systems under statistical, adversarial, computational, economic, and lifecycle constraints.