Devdyuti Mazumder

Aheer Sravon, Md. Ibrahim, Devdyuti Mazumder et al.

Autonomous pricing algorithms are increasingly influencing competition in digital markets; however, their behavior under realistic demand conditions remains largely unexamined. This paper offers a thorough analysis of four pricing algorithms -- Q-Learning, PSO, Double DQN, and DDPG -- across three classic duopoly models (Logit, Hotelling, Linear) and under various demand-shock regimes created by auto-regressive processes. By utilizing profit- and price-based collusion indices, we investigate how the interactions among algorithms, market structure, and stochastic demand collaboratively influence competitive outcomes. Our findings reveal that reinforcement-learning algorithms often sustain supra-competitive prices under stable demand, with DDPG demonstrating the most pronounced collusive tendencies. Demand shocks produce notably varied effects: Logit markets suffer significant performance declines, Hotelling markets remain stable, and Linear markets experience shock-induced profit inflation. Despite marked changes in absolute performance, the relative rankings of the algorithms are consistent across different environments. These results underscore the critical importance of market structure and demand uncertainty in shaping algorithmic competition, while also contributing to the evolving policy discussions surrounding autonomous pricing behavior.

Aheer Sravon, Devdyuti Mazumder, Md. Ibrahim

Distribution shifts and minority subpopulations frequently undermine the reliability of deep neural networks trained using Empirical Risk Minimization (ERM). Distributionally Robust Optimization (DRO) addresses this by optimizing for the worst-case risk within a neighborhood of the training distribution. However, conventional methods depend on a single, global robustness budget, which can lead to overly conservative models or a misallocation of robustness. We propose a variance-driven, adaptive, sample-level DRO (Var-DRO) framework that automatically identifies high-risk training samples and assigns a personalized robustness budget to each based on its online loss variance. Our formulation employs two-sided, KL-divergence-style bounds to constrain the ratio between adversarial and empirical weights for every sample. This results in a linear inner maximization problem over a convex polytope, which admits an efficient water-filling solution. To stabilize training, we introduce a warmup phase and a linear ramp schedule for the global cap on per-sample budgets, complemented by label smoothing for numerical robustness. Evaluated on CIFAR-10-C (corruptions), our method achieves the highest overall mean accuracy compared to ERM and KL-DRO. On Waterbirds, Var-DRO improves overall performance while matching or surpassing KL-DRO. On the original CIFAR-10 dataset, Var-DRO remains competitive, exhibiting the modest trade-off anticipated when prioritizing robustness. The proposed framework is unsupervised (requiring no group labels), straightforward to implement, theoretically sound, and computationally efficient.