Thepartially observableMarkovdecision process (POMDP) provides ageneral framework for modeling an agent's decision process with state uncertainty, and online planning plays a pivotal role in solving it. A belief is a distribution of states representing state uncertainty. Methods forlarge-scale POMDP problems rely on the same idea of sampling both states and observations.

Real Time Dynamic Programming (RTDP) is an online algorithm based on Dynamic Programming (DP) that acts by 1-step greedy planning.

Real Time Dynamic Programming (RTDP) is an online algorithm based on Dynamic Programming (DP) that acts by 1-step greedy planning. Unlike DP, RTDP does not require access to the entire state space, i.e., it explicitly handles the exploration. This fact makes RTDP particularly appealing when the state space is large and it is not possible to update all states simultaneously. In this we devise a multi-step greedy RTDP algorithm, which we call $h$-RTDP, that replaces the 1-step greedy policy with a $h$-step lookahead policy. We analyze $h$-RTDP in its exact form and establish that increasing the lookahead horizon, $h$, results in an improved sample complexity, with the cost of additional computations. This is the first work that proves improved sample complexity as a result of {\em increasing} the lookahead horizon in online planning. We then analyze the performance of $h$-RTDP in three approximate settings: approximate model, approximate value updates, and approximate state representation. For these cases, we prove that the asymptotic performance of $h$-RTDP remains the same as that of a corresponding approximate DP algorithm, the best one can hope for without further assumptions on the approximation errors.

Dynamic job shop scheduling, a fundamental combinatorial optimisation problem in various industrial sectors, poses substantial challenges for effective scheduling due to frequent disruptions caused by the arrival of new jobs. State-of-the-art methods employ machine learning to learn scheduling policies offline, enabling rapid responses to dynamic events. However, these offline policies are often imperfect, necessitating the use of planning techniques such as Monte Carlo Tree Search (MCTS) to improve performance at online decision time. The unpredictability of new job arrivals complicates online planning, as decisions based on incomplete problem information are vulnerable to disturbances. To address this issue, we propose the Dynamic Robust MCTS (DyRo-MCTS) approach, which integrates action robustness estimation into MCTS. DyRo-MCTS guides the production environment toward states that not only yield good scheduling outcomes but are also easily adaptable to future job arrivals. Extensive experiments show that DyRo-MCTS significantly improves the performance of offline-learned policies with negligible additional online planning time. Moreover, DyRo-MCTS consistently outperforms vanilla MCTS across various scheduling scenarios. Further analysis reveals that its ability to make robust scheduling decisions leads to long-term, sustainable performance gains under disturbances.

Online planning in Markov Decision Processes (MDPs) enables agents to make sequential decisions by simulating future trajectories from the current state, making it well-suited for large-scale or dynamic environments. Sample-based methods such as Sparse Sampling and Monte Carlo Tree Search (MCTS) are widely adopted for their ability to approximate optimal actions using a generative model. However, in practical settings, the generative model is often learned from limited data, introducing approximation errors that can degrade performance or lead to unsafe behaviors. To address these challenges, Robust MDPs (RMDPs) offer a principled framework for planning under model uncertainty, yet existing approaches are typically computationally intensive and not suited for real-time use. In this work, we introduce Robust Sparse Sampling (RSS), the first online planning algorithm for RMDPs with finite-sample theoretical performance guarantees. Unlike Sparse Sampling, which estimates the nominal value function, RSS computes a robust value function by leveraging the efficiency and theoretical properties of Sample Average Approximation (SAA), enabling tractable robust policy computation in online settings. RSS is applicable to infinite or continuous state spaces, and its sample and computational complexities are independent of the state space size. We provide theoretical performance guarantees and empirically show that RSS outperforms standard Sparse Sampling in environments with uncertain dynamics.

We consider an online variant of the fuel-constrained UAV routing problem with a ground-based mobile refueling station (FCURP-MRS), where targets incur unknown fuel costs. We develop a two-phase solution: an offline heuristic-based planner computes initial UAV and UGV paths, and a novel online planning algorithm that dynamically adjusts rendezvous points based on real-time fuel consumption during target processing. Preliminary Gazebo simulations demonstrate the feasibility of our approach in maintaining UAV-UGV path validity, ensuring mission completion. Link to video: https://youtu.be/EmpVj-fjqNY

Additional Feedback: COMMENTS AFTER REBUTTAL Thank you for your response. However, in this paper's case I find that the significance of the paper (i.e., support for your claim that "theoretical results provided in this work are important on their own") is severely lacking without experiments showing a link between this theory and an algorithm's performance in terms of measures like running time, number of 1-step Bellman backups, etc. ***Note: this is not a claim that every theoretical paper needs experiments; it applies only to this specific work, due to the theory issues mentioned in the original review.*** The rebuttal's attempted arguments against providing experiments really miss the mark: -- The rebuttal gives the "Beyond the one step greedy approach in RL" as an example of a paper similar in the degree of its theoretical focus to this submission, but that paper actually has experiments! Light experiments could do the job. That "Beyond the one step greedy approach in RL" paper that you mentioned yourself is a case in point.