Mahdi Salmani
Publications
Differentiating Through Dual Prices: End-to-End Policy Learning Under Capacity Constraints
Many social services assign scarce resources, such as housing assistance or hospital interventions, to people who arrive one at a time: each arrival must receive a decision immediately, and the long-run usage of every resource must stay within its capacity. We study how to learn such an assignment policy from logged observational data. The standard pipeline is decision-blind: fit one outcome model per arm by regression, price each capacitated resource from the fitted models, and assign each arrival the arm whose predicted outcome minus price is largest. We instead train the outcome models end-to-end, differentiating an off-policy estimate of the deployed policy's value through the dual prices themselves. We study two formulations: an exact nonconvex one, and a convex relaxation whose optimum always satisfies the capacity constraints in expectation and which is suboptimal by at most a term linear in the smoothing temperature and logarithmic in the number of arms. Every method is evaluated in a queueing simulation with resources replenished at their capacity rates. Across six datasets, the two end-to-end variants take the top slots on a deployment-adjusted value index at every delay cost, including zero; when capacities are binding, decision-blind baselines frequently violate them and incur much longer queueing delays. On the largest dataset, a hospital cohort of seventy thousand patients, end-to-end training also achieves significantly higher policy value, a margin that survives a capacity-matched neural baseline. Flexible decision-blind regression remains the stronger pure predictor where ground truth is measurable; end-to-end training is best suited to settings where resources are genuinely scarce and feasibility matters.
Early Stopping for Large Reasoning Models via Confidence Dynamics
Large reasoning models rely on long chain-of-thought generation to solve complex problems, but extended reasoning often incurs substantial computational cost and can even degrade performance due to overthinking. A key challenge is determining when the model should stop reasoning and produce the final answer. In this work, we study the confidence of intermediate answers during reasoning and observe two characteristic behaviors: correct reasoning trajectories often reach high-confidence answers early, while incorrect rollouts tend to produce long, unproductive reasoning traces and exhibit less reliable confidence dynamics. Motivated by these observations, we propose CoDE-Stop (Confidence Dynamics Early Stop), an early stopping method that leverages the dynamics of intermediate answer confidence to decide when to terminate reasoning, requiring no additional training and easily integrating into existing models. We evaluate CoDE-Stop on diverse reasoning and science benchmarks across multiple models. Compared to prior early stopping methods, it achieves a more favorable accuracy-compute tradeoff and reduces total token usage by 25-50% compared to standard full-length reasoning. In addition, we provide analyses of confidence dynamics during reasoning, offering insights into how confidence changes in both correct and incorrect trajectories.