This thesis investigates how interaction can be used as self-supervision to learn structured state representations that simplify downstream tasks. We formalize two inductive biases naturally present in the trajectories generated by agents that interact with their environment: geometry and temporal consistency of the underlying state space. We show that injecting these biases into representation learning yields additional, taskrelevant properties. First, we focus on geometric bias: we learn translationally equivariant latent spaces from images in which agent actions correspond to vector additions. We show how these representations can be used to estimate a recovery policy that mitigates the compounding of error in data-driven sequential decision-making policies. We further extend equivariant representations to scenes with external objects. Under an interaction-by-contact model, we prove that aligning the object’s and the agent’s latent embeddings yields an isometric, disentangled representation of both. Second, we relax the geometry assumption and explore the milder temporal consistency bias. This allows us to construct representations where the temporal order between states is preserved, a property we refer to as distance monotonicity. In the reinforcement learning setting, we show that, under suitable conditions, this property is enough to recover an approximation of the value function and provably estimate an optimal policy. In a multiple-sensor framework, these representations can be used to construct a Bayesian filtering state estimate robust under unknown noise. Lastly, we extend the concept of interactions from physical systems to the parametric space of a learner. We show how distance monotonic representations of the parameters of a model can be used to approximate the posterior distribution of a Bayesian neural network. Finally,in a meta-learning setting, we explore implicit representations of the learner to reduce the variance of a fast-adaptation model. Collectively, these results demonstrate that interaction-driven biases produce structured representations that simplify or enhance the learning process.
Alfredo Reichlin (Thu,) studied this question.