Jacek Karwowski

Raymond Douglas, Jacek Karwowski, Chan Bae et al.

There is increasing focus on adapting predictive models into agent-like systems, most notably AI assistants based on language models. We outline two structural reasons for why these models can fail when turned into agents. First, we discuss auto-suggestive delusions. Prior work has shown theoretically that models fail to imitate agents that generated the training data if the agents relied on hidden observations: the hidden observations act as confounding variables, and the models treat actions they generate as evidence for nonexistent observations. Second, we introduce and formally study a related, novel limitation: predictor-policy incoherence. When a model generates a sequence of actions, the model's implicit prediction of the policy that generated those actions can serve as a confounding variable. The result is that models choose actions as if they expect future actions to be suboptimal, causing them to be overly conservative. We show that both of those failures are fixed by including a feedback loop from the environment, that is, re-training the models on their own actions. We give simple demonstrations of both limitations using Decision Transformers and confirm that empirical results agree with our conceptual and formal analysis. Our treatment provides a unifying view of those failure modes, and informs the question of why fine-tuning offline learned policies with online learning makes them more effective.

Jacek Karwowski, Raymond Douglas

We investigate mathematically the notion of incoherence: a structural issue with reinforcement learning policies derived by naive goal-conditioning of autoregressive models. We focus on the process of re-training models on their own actions, that is, fine-tuning offline-learned policies with online RL. We prove that it decreases incoherence and leads to an improvement in return, and we aim to characterize the resulting trajectory of policies. By re-framing standard notions of control-as-inference and soft Q learning, we establish a three-way correspondence with two other ways of understanding the iterative re-training process: as folding the posterior into the reward and, in the deterministic case, as decreasing the temperature parameter; the correspondence has computational content via the training-inference trade-off. Through soft-conditioning generative models, we discuss the link between incoherence and the effective horizon.

Jacek Karwowski, Frank Nielsen

The extended Gaussian family is the closure of the Gaussian family obtained by completing the Gaussian family with the counterpart elements induced by degenerate covariance or degenerate precision matrices, or a mix of both degeneracies. The parameter space of the extended Gaussian family forms a symmetric positive semi-definite matrix bicone, i.e. two partial symmetric positive semi-definite matrix cones joined at their bases. In this paper, we study the Hilbert geometry of such an open bounded convex symmetric positive-definite bicone. We report the closed-form formula for the corresponding Hilbert metric distance and study exhaustively its invariance properties. We also touch upon potential applications of this geometry for dealing with extended Gaussian distributions.