Neural Multivariate Regression: Qualitative Insights from the Unconstrained Feature Model

The Unconstrained Feature Model (UFM) is a mathematical framework that enables closed-form approximations for minimal training loss and related performance measures in deep neural networks (DNNs). This paper leverages the UFM to provide qualitative insights into neural multivariate regression, a critical task in imitation learning, robotics, and reinforcement learning. Specifically, we address two key questions: (1) How do multi-task models compare to multiple single-task models in terms of training performance? (2) Can whitening and normalizing regression targets improve training performance? The UFM theory predicts that multi-task models achieve strictly smaller training MSE than multiple single-task models when the same or stronger regularization is applied to the latter, and our empirical results confirm these findings. Regarding whitening and normalizing regression targets, the UFM theory predicts that they reduce training MSE when the average variance across the target dimensions is less than one, and our empirical results once again confirm these findings. These findings highlight the UFM as a powerful framework for deriving actionable insights into DNN design and data pre-processing strategies.

Self-Confirming Transformer for Locally Consistent Online Adaptation in Multi-Agent Reinforcement Learning

Offline reinforcement learning (RL) leverages previously collected data to extract policies that return satisfying performance in online environments. However, offline RL suffers from the distribution shift between the offline dataset and the online environment. In the multi-agent RL (MARL) setting, this distribution shift may arise from the nonstationary opponents (exogenous agents beyond control) in the online testing who display distinct behaviors from those recorded in the offline dataset. Hence, the key to the broader deployment of offline MARL is the online adaptation to nonstationary opponents. Recent advances in large language models have demonstrated the surprising generalization ability of the transformer architecture in sequence modeling, which prompts one to wonder \textit{whether the offline-trained transformer policy adapts to nonstationary opponents during online testing}. This work proposes the self-confirming loss (SCL) in offline transformer training to address the online nonstationarity, which is motivated by the self-confirming equilibrium (SCE) in game theory. The gist is that the transformer learns to predict the opponents' future moves based on which it acts accordingly. As a weaker variant of Nash equilibrium (NE), SCE (equivalently, SCL) only requires local consistency: the agent's local observations do not deviate from its conjectures, leading to a more adaptable policy than the one dictated by NE focusing on global optimality. We evaluate the online adaptability of the self-confirming transformer (SCT) by playing against nonstationary opponents employing a variety of policies, from the random one to the benchmark MARL policies. Experimental results demonstrate that SCT can adapt to nonstationary opponents online, achieving higher returns than vanilla transformers and offline MARL baselines.