Partially observable Markov decision processes (POMDPs) are used to model a wide range of applications, including robotics, autonomous vehicles, and subsurface problems. However, accurately representing the belief is difficult for POMDPs with high-dimensional states. In this paper, we propose a novel approach that uses conditional deep generative models (cDGMs) to represent the belief. Unlike traditional belief representations, cDGMs are well-suited for high-dimensional states and large numbers of observations, and they can generate an arbitrary number of samples from the posterior belief. We train the cDGMs on data produced by random rollout trajectories and show their effectiveness in solving a mineral exploration POMDP with a large and continuous state space. The cDGMs outperform particle filter baselines in both task-agnostic measures of belief accuracy as well as in planning performance.

We consider data-driven inventory and pricing decisions in the feature-based newsvendor problem, where demand is influenced by both price and contextual features and is modeled without any structural assumptions. The unknown demand distribution results in a challenging conditional stochastic optimization problem, further complicated by decision-dependent uncertainty and the integration of features. Inspired by recent advances in deep generative learning, we propose a novel approach leveraging conditional deep generative models (cDGMs) to address these challenges. cDGMs learn the demand distribution and generate probabilistic demand forecasts conditioned on price and features. This generative approach enables accurate profit estimation and supports the design of algorithms for two key objectives: (1) optimizing inventory for arbitrary prices, and (2) jointly determining optimal pricing and inventory levels. We provide theoretical guarantees for our approach, including the consistency of profit estimation and convergence of our decisions to the optimal solution. Extensive simulations-ranging from simple to complex scenarios, including one involving textual features-and a real-world case study demonstrate the effectiveness of our approach. Our method opens a new paradigm in management science and operations research, is adaptable to extensions of the newsvendor and pricing problems, and holds potential for solving other conditional stochastic optimization problems.