Online Learning for Multi-Layer Hierarchical Inference under Partial and Policy-Dependent Feedback

Hierarchical inference systems route tasks across multiple computational layers, where each node may either finalize a prediction locally or offload the task to a node in the next layer for further processing. Learning optimal routing policies in such systems is challenging: inference loss is defined recursively across layers, while feedback on prediction error is revealed only at a terminal oracle layer. This induces a partial, policy-dependent feedback structure in which observability probabilities decay with depth, causing importance-weighted estimators to suffer from amplified variance. We study online routing for multi-layer hierarchical inference under long-term resource constraints and terminal-only feedback. We formalize the recursive loss structure and show that naive importance-weighted contextual bandit methods become unstable as feedback probability decays along the hierarchy. To address this, we develop a variance-reduced EXP4-based algorithm integrated with Lyapunov optimization, yielding unbiased loss estimation and stable learning under sparse and policy-dependent feedback. We provide regret guarantees relative to the best fixed routing policy in hindsight and establish near-optimality under stochastic arrivals and resource constraints. Experiments on large-scale multi-task workloads demonstrate improved stability and performance compared to standard importance-weighted approaches.

Optimal Resource Allocation for ML Model Training and Deployment under Concept Drift

We study how to allocate resources for training and deployment of machine learning (ML) models under concept drift and limited budgets. We consider a setting in which a model provider distributes trained models to multiple clients whose devices support local inference but lack the ability to retrain those models, placing the burden of performance maintenance on the provider. We introduce a model-agnostic framework that captures the interaction between resource allocation, concept drift dynamics, and deployment timing. We show that optimal training policies depend critically on the aging properties of concept durations. Under sudden concept changes, we derive optimal training policies subject to budget constraints when concept durations follow distributions with Decreasing Mean Residual Life (DMRL), and show that intuitive heuristics are provably suboptimal under Increasing Mean Residual Life (IMRL). We further study model deployment under communication constraints, prove that the associated optimization problem is quasi-convex under mild conditions, and propose a randomized scheduling strategy that achieves near-optimal client-side performance. These results offer theoretical and algorithmic foundations for cost-efficient ML model management under concept drift, with implications for continual learning, distributed inference, and adaptive ML systems.