Jason Bohne

Haohan Xu, Jason Bohne, Pawel Polak et al.

We study the detection of transient liquidity erosion ("crumbling quotes") in electronic limit order books, where observable quote deterioration may reflect either mechanical liquidity withdrawal or informational repricing. Using the ABIDES agent-based simulator, we construct a multi-agent environment in which crumbling emerges from stochastic regime switches in a market maker, providing time-resolved ground truth unavailable in real market data. We develop a detection pipeline that identifies mechanically driven quote erosion using order book features, and train a neural model to produce calibrated crumbling probabilities. Experiments demonstrate that the proposed framework reliably identifies crumbling events against agent-level ground truth, with the neural model achieving +36% AUC improvement over rule-based baselines and robust performance across normal, high-volatility, bull, and bear market conditions. Ablation studies on temporal features and varying the dependence structure of the ground-truth mechanism confirm that the framework generalizes across both independent and autocorrelated liquidity withdrawal dynamics.

Jason Bohne, David Rosenberg, Gary Kazantsev et al.

Bilevel optimization methods are increasingly relevant within machine learning, especially for tasks such as hyperparameter optimization and meta-learning. Compared to the offline setting, online bilevel optimization (OBO) offers a more dynamic framework by accommodating time-varying functions and sequentially arriving data. This study addresses the online nonconvex-strongly convex bilevel optimization problem. In deterministic settings, we introduce a novel online Bregman bilevel optimizer (OBBO) that utilizes adaptive Bregman divergences. We demonstrate that OBBO enhances the known sublinear rates for bilevel local regret through a novel hypergradient error decomposition that adapts to the underlying geometry of the problem. In stochastic contexts, we introduce the first stochastic online bilevel optimizer (SOBBO), which employs a window averaging method for updating outer-level variables using a weighted average of recent stochastic approximations of hypergradients. This approach not only achieves sublinear rates of bilevel local regret but also serves as an effective variance reduction strategy, obviating the need for additional stochastic gradient samples at each timestep. Experiments on online hyperparameter optimization and online meta-learning highlight the superior performance, efficiency, and adaptability of our Bregman-based algorithms compared to established online and offline bilevel benchmarks.

Jason Bohne, Ieva Petrulionyte, Michael Arbel et al.

Functional bilevel optimization (FBO) provides a powerful framework for hierarchical learning in function spaces, yet current methods are limited to static offline settings and perform suboptimally in online, non-stationary scenarios. We propose SmoothFBO, the first algorithm for non-stationary FBO with both theoretical guarantees and practical scalability. SmoothFBO introduces a time-smoothed stochastic hypergradient estimator that reduces variance through a window parameter, enabling stable outer-loop updates with sublinear regret. Importantly, the classical parametric bilevel case is a special reduction of our framework, making SmoothFBO a natural extension to online, non-stationary settings. Empirically, SmoothFBO consistently outperforms existing FBO methods in non-stationary hyperparameter optimization and model-based reinforcement learning, demonstrating its practical effectiveness. Together, these results establish SmoothFBO as a general, theoretically grounded, and practically viable foundation for bilevel optimization in online, non-stationary scenarios.

Jason Bohne, Pawel Polak, David Rosenberg et al.

Direct Preference Optimization (DPO) has recently emerged as a simple and effective alternative to reinforcement learning from human feedback (RLHF) for aligning large language models (LLMs) with user preferences. However, existing DPO formulations rely on a single monolithic model, which limits their expressivity in multi-task settings and their adaptability to heterogeneous or diverse preference distributions. In this work, we propose Mix- and MoE-DPO, a framework that extends DPO with both soft mixture models and mixture-of-experts (MoE) architectures, using a stochastic variational inference approach. Our method introduces a latent-variable model over expert assignments and optimizes a variational evidence lower bound (ELBO), enabling stable and efficient learning of specialized expert policies from preference data. Mix- and MoE-DPO provides three key advantages over standard DPO: (i) generalization via universal function approximation through mixtures; (ii) reward and policy specialization through expert components tailored to distinct preference modes; and (iii) contextual alignment through input-dependent soft gating that enables user-specific mixture policies. Our framework supports both shared base architectures with expert-specific policy heads and fully independent expert models, allowing flexible trade-offs between parameter efficiency and specialization. We validate our approach on a variety of model sizes and multi-preference datasets, demonstrating that Mix- and MoE-DPO offers a powerful and scalable method for preference-based LLM alignment.