According to Alg. 2, in each exploration, at least one leaf node will be expanded. Thus, we have the conclusion that AdaOPS is guaranteed to terminate. First, we will demonstrate that the value of any belief can be formulated as an integral. This lemma is a concentration inequality of self-normalized importance sampling estimator. The ESS threshold µ for adaptive resampling is set to .

Model-based planners for partially observable problems must accommodate both model uncertainty during planning and goal uncertainty during objective inference. However, model-based planners may be brittle under these types of uncertainty because they rely on an exact model and tend to commit to a single optimal behavior. Inspired by results in the model-free setting, we propose an entropy-regularized model-based planner for partially observable problems. Entropy regularization promotes policy robustness for planning and objective inference by encouraging policies to be no more committed to a single action than necessary. We evaluate the robustness and objective inference performance of entropy-regularized policies in three problem domains. Our results show that entropy-regularized policies outperform non-entropy-regularized baselines in terms of higher expected returns under modeling errors and higher accuracy during objective inference.

We study regret minimization for reinforcement learning (RL) in Latent Markov Decision Processes (LMDPs) with context in hindsight. We design a novel model-based algorithmic framework which can be instantiated with both a model-optimistic and a value-optimistic solver. We prove an $\tilde{O}(\sqrt{\mathsf{Var}^\star M \Gamma S A K})$ regret bound where $\tilde{O}$ hides logarithm factors, $M$ is the number of contexts, $S$ is the number of states, $A$ is the number of actions, $K$ is the number of episodes, $\Gamma \le S$ is the maximum transition degree of any state-action pair, and $\mathsf{Var}^\star$ is a variance quantity describing the determinism of the LMDP. The regret bound only scales logarithmically with the planning horizon, thus yielding the first (nearly) horizon-free regret bound for LMDP. This is also the first problem-dependent regret bound for LMDP. Key in our proof is an analysis of the total variance of alpha vectors (a generalization of value functions), which is handled with a truncation method. We complement our positive result with a novel $\Omega(\sqrt{\mathsf{Var}^\star M S A K})$ regret lower bound with $\Gamma = 2$, which shows our upper bound minimax optimal when $\Gamma$ is a constant for the class of variance-bounded LMDPs. Our lower bound relies on new constructions of hard instances and an argument inspired by the symmetrization technique from theoretical computer science, both of which are technically different from existing lower bound proof for MDPs, and thus can be of independent interest.

Optimizing a partially observable Markov decision process (POMDP) policy is challenging. The policy graph improvement (PGI) algorithm for POMDPs represents the policy as a fixed size policy graph and improves the policy monotonically. Due to the fixed policy size, computation time for each improvement iteration is known in advance. Moreover, the method allows for compact understandable policies. This report describes the technical details of the PGI [1] and particle based PGI [2] algorithms for POMDPs in a more accessible way than [1] or [2] allowing practitioners and students to understand and implement the algorithms.