The implementation of the following setup is written in JAX [6] and Haiku [35]. We use Residual Networks (ResNets) and Wide ResNets (WRNs) [31, 79]. This is consistent with prior work [30, 49, 60, 72, 82] which use diverse variants of these network families. Furthermore, we adopt the same architecture details as Gowal et al. [30] with Swish/SiLU [33] activation functions. Most of the experiments are conducted on a WRN-28-10 model which has a depth of 28, a width multiplier of 10 and contains 36M parameters. To evaluate the effect of using additional generated data on wider and deeper networks, we also run several experiments using WRN-70-16, which contains 267M parameters.

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse problems. We find that state-of-the-art training techniques are not well-suited to many problems that involve physical processes. The highly nonlinear behavior, common in physical processes, results in strongly varying gradients that lead first-order optimizers like SGD or Adam to compute suboptimal optimization directions. We propose a novel hybrid training approach that combines higherorder optimization methods with machine learning techniques. We take updates from a scale-invariant inverse problem solver and embed them into the gradientdescent-based learning pipeline, replacing the regular gradient of the physical process. We demonstrate the capabilities of our method on a variety of canonical physical systems, showing that it yields significant improvements on a wide range of optimization and learning problems.

Reinforcement learning (RL) has shown great promise for developing dialogue1 management (DM) agents that are non-myopic, conduct rich conversations, and2 maximize overall user satisfaction. Despite recent developments in RL and lan-3 guage models (LMs), using RL to power conversational chatbots remains challeng-4 ing, in part because RL requires online exploration to learn effectively, whereas5 collecting novel human-bot interactions can be expensive and unsafe. This issue is6 exacerbated by the combinatorial action spaces facing these algorithms, as most7 LM agents generate responses at the word level. We develop a variety of RL algo-8 rithms, specialized to dialogue planning, that leverage recent Mixture-of-Expert9 Language Models (MoE-LMs)--models that capture diverse semantics, generate10 utterances reflecting different intents, and are amenable for multi-turn DM. By11 exploiting MoE-LM structure, our methods significantly reduce the size of the12 action space and improve the efficacy of RL-based DM.