Lukas Haverbeck

Pierre-François Massiani, Alexander von Rohr, Lukas Haverbeck et al.

Despite the many recent advances in reinforcement learning (RL), the question of learning policies that robustly satisfy state constraints under unknown disturbances remains open. In this paper, we offer a new perspective on achieving robust safety by analyzing the interplay between two well-established techniques in model-free RL: entropy regularization, and constraints penalization. We reveal empirically that entropy regularization in constrained RL inherently biases learning toward maximizing the number of future viable actions, thereby promoting constraints satisfaction robust to action noise. Furthermore, we show that by relaxing strict safety constraints through penalties, the constrained RL problem can be approximated arbitrarily closely by an unconstrained one and thus solved using standard model-free RL. This reformulation preserves both safety and optimality while empirically improving resilience to disturbances. Our results indicate that the connection between entropy regularization and robustness is a promising avenue for further empirical and theoretical investigation, as it enables robust safety in RL through simple reward shaping.

Pierre-François Massiani, Christian Fiedler, Lukas Haverbeck et al.

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals differ with high probability, and include tests of conditional moments or two-sample tests. Our key idea is to transform confidence bounds of a learning method into a test of conditional expectations. We instantiate this principle for kernel ridge regression (KRR) with subgaussian noise. An intermediate data embedding then enables more general tests -- including conditional two-sample tests -- via kernel mean embeddings of distributions. To have guarantees in this setting, we generalize existing pointwise-in-time or time-uniform confidence bounds for KRR to previously-inaccessible yet essential cases such as infinite-dimensional outputs with non-trace-class kernels. These bounds also circumvent the need for independent data, allowing for instance online sampling. To make our tests readily applicable in practice, we introduce bootstrapping schemes leveraging the parametric form of testing thresholds identified in theory to avoid tuning inaccessible parameters. We illustrate the tests on examples, including one in process monitoring and comparison of dynamical systems. Overall, our results establish a comprehensive foundation for conditional testing on functionals, from theoretical guarantees to an algorithmic implementation, and advance the state of the art on confidence bounds for vector-valued least squares estimation.