Terminal feedback in multi-turn agent training leaves both rollout allocation and local credit underdetermined. Dynamics-Predictive Sampling (DPS) [9] provides a task-level predictive sampling reference, but interactive agents also need to choose which visited states merit further continuations. We introduce TSBPO with two method components. A lightweight, fine-grained Root/Branch budget allocator distributes factual rollouts across tasks and additional suffixes across replayable states using likelihood-fitted estimates of terminal-outcome contrast. On the resulting physical rollout trees, a tree-aware step-level credit assignment algorithm compares immediate sibling segments and assigns their local outcome contrasts to the turns they contain. Exact task/observation groups provide a complementary step term. The allocator selects what to sample; observed outcomes determine the subsequent credit. With a Qwen2.5-1.5B actor, fixed checkpoints attain 97.79% seen and 96.64% unseen stochastic success on ALFWorld, and an 81.07% per-episode success rate over six stochastic episodes for each of the 500 WebShop test goals. At the WebShop update-100 checkpoint, removing the observation-group step term yields 75.93% under the same evaluation. These results describe the evaluated training configurations on two interactive benchmarks.
We propose an optimization-informed deep neural network approach, named iUzawa-Net, aiming for the first solver that enables real-time solutions for a class of nonsmooth optimal control problems of linear partial differential equations (PDEs). The iUzawa-Net unrolls an inexact Uzawa method for saddle point problems, replacing classical preconditioners and PDE solvers with specifically designed learnable neural networks. We prove universal approximation properties and establish the asymptotic $\varepsilon$-optimality for the iUzawa-Net, and validate its promising numerical efficiency through nonsmooth elliptic and parabolic optimal control problems. Our techniques offer a versatile framework for designing and analyzing various optimization-informed deep learning approaches to optimal control and other PDE-constrained optimization problems. The proposed learning-to-control approach synergizes model-based optimization algorithms and data-driven deep learning techniques, inheriting the merits of both methodologies.