This paper investigates Reinforcement Learning (RL) approaches to enhance the reasoning capabilities of Large Language Model (LLM) agents in long-horizon, multi-turn scenarios. Although RL algorithms such as Group Relative Policy Optimization (GRPO) and Proximal Policy Optimization (PPO) have been widely applied to train multi-turn LLM agents, they typically rely only on sparse outcome rewards and lack dense intermediate signals across multiple decision steps, limiting their performance on complex reasoning tasks. To bridge this gap, we present the first systematic study of \textit{turn-level reward design} for multi-turn RL algorithms and agent applications. By integrating turn-level rewards, we extend GRPO and PPO to their respective multi-turn variants, enabling fine-grained credit assignment. We conduct case studies on multi-turn reasoning-augmented search agents, where we carefully design two types of turn-level rewards: verifiable and LLM-as-judge. Our experiments on multi-turn search tasks demonstrate that incorporating well-designed turn-level rewards enables RL algorithms to significantly outperform baseline methods with trajectory-level rewards. Both training and validation reward curves illustrate that our method achieves \textit{greater stability}, \textit{faster convergence}, and \textit{higher accuracy}. Numerical results across diverse question-answering datasets further show that our approach consistently delivers highest answer correctness and 100\% format correctness.

Reinforcement learning (RL) holds significant promise for training LLM agents to handle complex, goal-oriented tasks that require multi-step interactions with external environments. However, a critical challenge when applying RL to these agentic tasks arises from delayed rewards: feedback signals are typically available only after the entire task is completed. This makes it non-trivial to assign delayed rewards to earlier actions, providing insufficient guidance regarding environmental constraints and hindering agent training. In this work, we draw on the insight that the ultimate completion of a task emerges from the cumulative progress an agent makes across individual steps. We propose Stepwise Progress Attribution (SPA), a general reward redistribution framework that decomposes the final reward into stepwise contributions, each reflecting its incremental progress toward overall task completion. To achieve this, we train a progress estimator that accumulates stepwise contributions over a trajectory to match the task completion. During policy optimization, we combine the estimated per-step contribution with a grounding signal for actions executed in the environment as the fine-grained, intermediate reward for effective agent training. Extensive experiments on common agent benchmarks (including Webshop, ALFWorld, and VirtualHome) demonstrate that SPA consistently outperforms the state-of-the-art method in both success rate (+2.5\% on average) and grounding accuracy (+1.9\% on average). Further analyses demonstrate that our method remarkably provides more effective intermediate rewards for RL training. Our code is available at https://github.com/WangHanLinHenry/SPA-RL-Agent.

Monte Carlo Tree Search (MCTS) has emerged as a powerful tool for decision-making in robotics, enabling efficient exploration of large search spaces. However, traditional MCTS methods struggle in environments characterized by high uncertainty and noisy data due to their reliance on final-step reward evaluation. The lack of intermediate feedback during search often results in suboptimal decision-making and computational inefficiencies. This paper introduces Reward-Centered ReST-MCTS, a novel framework that enhances MCTS by incorporating intermediate reward shaping. The core of our approach is the Rewarding Center, which refines search trajectories by dynamically assigning partial rewards using rule-based validation, heuristic guidance, and neural estimation. By integrating these mechanisms, our method enables real-time optimization of search paths, mitigating the effects of error propagation. We evaluate Reward-Centered ReST-MCTS in robotic manipulation tasks under high uncertainty, demonstrating consistent improvements in decision accuracy. Compared to baseline methods, including Chain-of-Thought (CoT) prompting and Vanilla ReST-MCTS, our framework achieves a 2-4% accuracy improvement while maintaining computational feasibility. Ablation studies confirm the effectiveness of intermediate feedback in search refinement, particularly in pruning incorrect decision paths early. Furthermore, robustness tests show that our method retains high performance across varying levels of uncertainty.

Diffusion models produce impressive results in modalities ranging from images and video to protein design and text. However, generating samples with user-specified properties remains a challenge. Recent research proposes fine-tuning models to maximize rewards that capture desired properties, but these methods require expensive training and are prone to mode collapse. In this work, we propose Feynman Kac (FK) steering, an inference-time framework for steering diffusion models with reward functions. FK steering works by sampling a system of multiple interacting diffusion processes, called particles, and resampling particles at intermediate steps based on scores computed using functions called potentials. Potentials are defined using rewards for intermediate states and are selected such that a high value indicates that the particle will yield a high-reward sample. We explore various choices of potentials, intermediate rewards, and samplers. We evaluate FK steering on text-to-image and text diffusion models. For steering text-to-image models with a human preference reward, we find that FK steering a 0.8B parameter model outperforms a 2.6B parameter fine-tuned model on prompt fidelity, with faster sampling and no training. For steering text diffusion models with rewards for text quality and specific text attributes, we find that FK steering generates lower perplexity, more linguistically acceptable outputs and enables gradient-free control of attributes like toxicity. Our results demonstrate that inference-time scaling and steering of diffusion models, even with off-the-shelf rewards, can provide significant sample quality gains and controllability benefits. Code is available at https://github.com/zacharyhorvitz/Fk-Diffusion-Steering .

There is a surge of interest in using formal languages such as Linear Temporal Logic (LTL) and finite automata to precisely and succinctly specify complex tasks and derive reward functions for reinforcement learning (RL) in robotic applications. However, existing methods often assign sparse rewards (e.g., giving a reward of 1 only if a task is completed and 0 otherwise), necessitating extensive exploration to converge to a high-quality policy. To address this limitation, we propose a suite of reward functions that incentivize an RL agent to make measurable progress on tasks specified by LTL formulas and develop an adaptive reward shaping approach that dynamically updates these reward functions during the learning process. Experimental results on a range of RL-based robotic tasks demonstrate that the proposed approach is compatible with various RL algorithms and consistently outperforms baselines, achieving earlier convergence to better policies with higher task success rates and returns.

Most medical treatment decisions are sequential in nature. Hence, there is substantial hope that reinforcement learning may make it possible to formulate precise data-driven treatment plans. However, a key challenge for most applications in this field is the sparse nature of primarily mortality-based reward functions, leading to decreased stability of offline estimates. In this work, we introduce a deep Q-learning approach able to obtain more reliable critical care policies. This method integrates relevant but noisy intermediate biomarker signals into the reward specification, without compromising the optimization of the main outcome of interest (e.g. patient survival). We achieve this by first pruning the action set based on all available rewards, and second training a final model based on the sparse main reward but with a restricted action set. By disentangling accurate and approximated rewards through action pruning, potential distortions of the main objective are minimized, all while enabling the extraction of valuable information from intermediate signals that can guide the learning process. We evaluate our method in both off-policy and offline settings using simulated environments and real health records of patients in intensive care units. Our empirical results indicate that pruning significantly reduces the size of the action space while staying mostly consistent with the actions taken by physicians, outperforming the current state-of-the-art offline reinforcement learning method conservative Q-learning. Our work is a step towards developing reliable policies by effectively harnessing the wealth of available information in data-intensive critical care environments.

In reinforcement learning, the objective is almost always defined as a \emph{cumulative} function over the rewards along the process. However, there are many optimal control and reinforcement learning problems in various application fields, especially in communications and networking, where the objectives are not naturally expressed as summations of the rewards. In this paper, we recognize the prevalence of non-cumulative objectives in various problems, and propose a modification to existing algorithms for optimizing such objectives. Specifically, we dive into the fundamental building block for many optimal control and reinforcement learning algorithms: the Bellman optimality equation. To optimize a non-cumulative objective, we replace the original summation operation in the Bellman update rule with a generalized operation corresponding to the objective. Furthermore, we provide sufficient conditions on the form of the generalized operation as well as assumptions on the Markov decision process under which the globally optimal convergence of the generalized Bellman updates can be guaranteed. We demonstrate the idea experimentally with the bottleneck objective, i.e., the objectives determined by the minimum reward along the process, on classical optimal control and reinforcement learning tasks, as well as on two network routing problems on maximizing the flow rates.

Abstract-- Designing appropriate reward functions for Reinforcement Learning (RL) approaches has been a significant problem, especially for complex environments such as Atari games. Utilizing natural language instructions to provide intermediate rewards to RL agents in a process known as reward shaping can help the agent in reaching the goal state faster. In this work, we propose a natural language-based reward shaping approach that maps trajectories from the Montezuma's Revenge game environment to corresponding natural language instructions using an extension of the LanguagE-Action Reward Network (LEARN) framework. These trajectory-language mappings are further used to generate intermediate rewards which are integrated into reward functions that can be utilized to learn an optimal policy for any standard RL algorithms. For a set of 15 tasks from Atari's Montezuma's Revenge game, the Ext-LEARN approach leads to the successful completion of tasks more often on average than the reward shaping approach that uses the LEARN framework and performs even better than the reward shaping framework without natural languagebased rewards. Reinforcement Learning (RL) has been used extensively in games with promising results in terms of performance. RL algorithms utilize the concepts of rewards (positive or negative reinforcements) to help agents in learning to optimize their behaviors in an environment with which they interact. Subsequently, RL has been successfully implemented in complex environments such as Atari games [1]. However, defining reward functions has been the most significant challenge in RL, especially while scaling RL algorithms for real-world applications with large state spaces.

The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given context and an action taken by an agent. In contrast to Bayesian optimization, the arguments of the function are not under agent's control, but are indirectly determined by the agent's action based on a given context. If the information of the features is to be included in the maximization problem, the full conditional distribution of such features, rather than its expectation only, needs to be accounted for. Furthermore, the function is itself unknown, only counting with noisy observations of such function, and potentially requiring the use of unmatched data sets. We propose a novel algorithm for the aforementioned problem which takes into consideration the uncertainty derived from the estimation of both the conditional distribution of the features and the unknown function, by modeling the former as a Bayesian conditional mean embedding and the latter as a Gaussian process. Our algorithm empirically outperforms the current state-of-the-art algorithm in the experiments conducted.