Neural networks have shown great predictive power when applied to unstructured data such as images and natural languages.

Probabilistic context-free grammars (PCFGs) and dynamic Bayesian networks (DBNs) are widely used sequence models with complementary strengths and limitations. While PCFGs allow for nested hierarchical dependencies (tree structures), their latent variables (non-terminal symbols) have to be discrete. In contrast, DBNs allow for continuous latent variables, but the dependencies are strictly sequential (chain structure). Therefore, neither can be applied if the latent variables are assumed to be continuous and also to have a nested hierarchical dependency structure. In this paper, we present Recursive Bayesian Networks (RBNs), which generalise and unify PCFGs and DBNs, combining their strengths and containing both as special cases. RBNs define a joint distribution over tree-structured Bayesian networks with discrete or continuous latent variables. The main challenge lies in performing joint inference over the exponential number of possible structures and the continuous variables. We provide two solutions: 1) For arbitrary RBNs, we generalise inside and outside probabilities from PCFGs to the mixed discrete-continuous case, which allows for maximum posterior estimates of the continuous latent variables via gradient descent, while marginalising over network structures.

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.