We study decision making with structured observation (DMSO). Previous work (Foster et al., 2021b, 2023a) has characterized the complexity of DMSO via the decision-estimation coefficient (DEC), but left a gap between the regret upper and lower bounds that scales with the size of the model class. To tighten this gap, Foster et al. (2023b) introduced optimistic DEC, achieving a bound that scales only with the size of the value-function class. However, their optimism-based exploration is only known to handle the stochastic setting, and it remains unclear whether it extends to the adversarial setting. We introduce Dig-DEC, a model-free DEC that removes optimism and drives exploration purely by information gain. Dig-DEC is always no larger than optimistic DEC and can be much smaller in special cases. Importantly, the removal of optimism allows it to handle adversarial environments without explicit reward estimators. By applying Dig-DEC to hybrid MDPs with stochastic transitions and adversarial rewards, we obtain the first model-free regret bounds for hybrid MDPs with bandit feedback under several general transition structures, resolving the main open problem left by Liu et al. (2025). We also improve the online function-estimation procedure in model-free learning: For average estimation error minimization, we refine the estimator in Foster et al. (2023b) to achieve sharper concentration, improving their regret bounds from $T^{3/4}$ to $T^{2/3}$ (on-policy) and from $T^{5/6}$ to $T^{7/9}$ (off-policy). For squared error minimization in Bellman-complete MDPs, we redesign their two-timescale procedure, improving the regret bound from $T^{2/3}$ to $\sqrt{T}$. This is the first time a DEC-based method achieves performance matching that of optimism-based approaches (Jin et al., 2021; Xie et al., 2023) in Bellman-complete MDPs.

Recent advances in solutions to Hybrid MDPs with discrete and continuous state and action spaces have significantly extended the class of MDPs for which exact solutions can be derived, albeit at the expense of a restricted transition noise model. In this paper, we work around limitations of previous solutions by adopting a robust optimization approach in which Nature is allowed to adversarially determine transition noise within pre-specified confidence intervals. This allows one to derive an optimal policy with an arbitrary (user-specified) level of success probability and significantly extends the class of transition noise models for which Hybrid MDPs can be solved. This work also significantly extends results for the related ``chance-constrained'' approach in stochastic hybrid control to accommodate state-dependent noise. We demonstrate our approach working on a variety of hybrid MDPs taken from AI planning, operations research, and control theory, noting that this is the first time robust solutions with strong guarantees over all states have been automatically derived for such problems.

We investigate the use of temporally abstract actions, or macro-actions, in the solution of Markov decision processes. Unlike current models that combine both primitive actions and macro-actions and leave the state space unchanged, we propose a hierarchical model (using an abstract MDP) that works with macro-actions only, and that significantly reduces the size of the state space. This is achieved by treating macroactions as local policies that act in certain regions of state space, and by restricting states in the abstract MDP to those at the boundaries of regions. The abstract MDP approximates the original and can be solved more efficiently. We discuss several ways in which macro-actions can be generated to ensure good solution quality. Finally, we consider ways in which macro-actions can be reused to solve multiple, related MDPs; and we show that this can justify the computational overhead of macro-action generation.