Dynamic Minimax Regret Optimization for Robust LLM Post-Training

Chengbo Zang, Haoyu Dong, Mehmet Kerem Turkcan, Gil Zussman, Zoran Kostic +1

Modern LLM training increasingly relies on heterogeneous data sources spanning different domains, tasks, preference distributions, and difficulty levels. We study dynamic minimax regret for group-distributionally robust LLM post-training under instantaneous mini-batch-only bandit feedback. The framework views the training as a two-player sampler-optimizer process: a sampler adaptively selects among data sources using bandit feedback, while an optimizer updates the model parameters using stochastic gradients from the selected source. We focus on the practically restrictive setting where source losses evolve with model training but historical data are not re-evaluated, requiring the sampler to track instantaneous worst-sources from stale partial feedback. We propose DUCB-OGD, a simple and scalable algorithm that couples a Discounted Upper-Confidence-Bound sampler with an Online Gradient Descent optimizer. The sampler maintains exponential moving average loss estimates and confidence radii based on discounted effective sample sizes, avoiding costly re-evaluation of past data or intrusive changes to standard training pipelines. For $K$ data sources and $T$ training steps, we prove…