Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for complex reasoning tasks with clear correctness signals such as math and coding. However, extending it to real-world reasoning tasks is challenging, as evaluation depends on nuanced, multi-criteria judgments rather than binary correctness. Instance-specific rubrics have recently been used in evaluation benchmarks to capture such judgments, but their potential as reward signals for on-policy post-training remains underexplored. We introduce $\textbf{Rubrics as Rewards}$ (RaR), an on-policy reinforcement learning method that extends RLVR beyond verifiable domains by using rubric-based feedback. Across both medical and science domains, we evaluate multiple strategies for aggregating rubric feedback into rewards. The best RaR variant achieves relative improvements of up to $31\%$ on HealthBench and $7\%$ on GPQA-Diamond over popular LLM-as-judge baselines that rely on direct Likert-based rewards. These results demonstrate that RaR-trained policies adapt well to diverse evaluation formats, performing strongly on both rubric-based and multiple-choice tasks. Moreover, we find that using rubrics as structured reward signals yields better alignment for smaller judges and reduces performance variance across judge scales.

Biological brains demonstrate complex neural activity, where neural dynamics are critical to how brains process information. Most artificial neural networks ignore the complexity of individual neurons. We challenge that paradigm. By incorporating neuron-level processing and synchronization, we reintroduce neural timing as a foundational element. We present the Continuous Thought Machine (CTM), a model designed to leverage neural dynamics as its core representation. The CTM has two innovations: (1) neuron-level temporal processing, where each neuron uses unique weight parameters to process incoming histories; and (2) neural synchronization as a latent representation. The CTM aims to strike a balance between neuron abstractions and biological realism. It operates at a level of abstraction that effectively captures essential temporal dynamics while remaining computationally tractable. We demonstrate the CTM's performance and versatility across a range of tasks, including solving 2D mazes, ImageNet-1K classification, parity computation, and more. Beyond displaying rich internal representations and offering a natural avenue for interpretation owing to its internal process, the CTM is able to perform tasks that require complex sequential reasoning. The CTM can also leverage adaptive compute, where it can stop earlier for simpler tasks, or keep computing when faced with more challenging instances. The goal of this work is to share the CTM and its associated innovations, rather than pushing for new state-of-the-art results. To that end, we believe the CTM represents a significant step toward developing more biologically plausible and powerful artificial intelligence systems. We provide an accompanying interactive online demonstration at https://pub.sakana.ai/ctm/ and an extended technical report at https://pub.sakana.ai/ctm/paper .

Partial observability is a notorious challenge in reinforcement learning (RL), due to the need to learn complex, history-dependent policies. Recent empirical successes have used privileged expert distillation--which leverages availability of latent state information during training (e.g., from a simulator) to learn and imitate the optimal latent, Markovian policy--to disentangle the task of "learning to see" from "learning to act". While expert distillation is more computationally efficient than RL without latent state information, it also has well-documented failure modes. In this paper--through a simple but instructive theoretical model called the perturbed Block MDP, and controlled experiments on challenging simulated locomotion tasks--we investigate the algorithmic trade-off between privileged expert distillation and standard RL without privileged information. Our main findings are: (1) The trade-off empirically hinges on the stochasticity of the latent dynamics, as theoretically predicted by contrasting approximate decodability with belief contraction in the perturbed Block MDP; and (2) The optimal latent policy is not always the best latent policy to distill. Our results suggest new guidelines for effectively exploiting privileged information, potentially advancing the efficiency of policy learning across many practical partially observable domains.

We study the Non-Stationary Reinforcement Learning (RL) under distribution shifts in both finite-horizon episodic and infinite-horizon discounted Markov Decision Processes (MDPs). In the finite-horizon case, the transition functions may suddenly change at a particular episode. In the infinite-horizon setting, such changes can occur at an arbitrary time step during the agent's interaction with the environment. While the Q-learning Upper Confidence Bound algorithm (QUCB) can discover a proper policy during learning, due to the distribution shifts, this policy can exploit sub-optimal rewards after the shift happens. To address this issue, we propose Density-QUCB (DQUCB), a shift-aware Q-learning~UCB algorithm, which uses a transition density function to detect distribution shifts, then leverages its likelihood to enhance the uncertainty estimation quality of Q-learning~UCB, resulting in a balance between exploration and exploitation. Theoretically, we prove that our oracle DQUCB achieves a better regret guarantee than QUCB. Empirically, our DQUCB enjoys the computational efficiency of model-free RL and outperforms QUCB baselines by having a lower regret across RL tasks, as well as a real-world COVID-19 patient hospital allocation task using a Deep-Q-learning architecture.

Humanoid robots, as general-purpose physical agents, must integrate both intelligent control and adaptive morphology to operate effectively in diverse real-world environments. While recent research has focused primarily on optimizing control policies for fixed robot structures, this position paper argues for evolving both control strategies and humanoid robots' physical structure under a co-design mechanism. Inspired by biological evolution, this approach enables robots to iteratively adapt both their form and behavior to optimize performance within task-specific and resource-constrained contexts. Despite its promise, co-design in humanoid robotics remains a relatively underexplored domain, raising fundamental questions about its feasibility and necessity in achieving true embodied intelligence. To address these challenges, we propose practical co-design methodologies grounded in strategic exploration, Sim2Real transfer, and meta-policy learning. We further argue for the essential role of co-design by analyzing it from methodological, application-driven, and community-oriented perspectives. Striving to guide and inspire future studies, we present open research questions, spanning from short-term innovations to long-term goals. This work positions co-design as a cornerstone for developing the next generation of intelligent and adaptable humanoid agents.

Abstract--In recent years, deep reinforcement learning (DRL) has gained traction for solving the NP-hard traveling salesman problem (TSP). However, limited attention has been given to the close-enough TSP (CETSP), primarily due to the challenge introduced by its neighborhood-based visitation criterion, wherein a node is considered visited if the agent enters a compact neighborhood around it. In this work, we formulate a Markov decision process (MDP) for CETSP using a discretization scheme and propose a novel unified dual-decoder DRL (UD3RL) framework that separates decision-making into node selection and waypoint determination. Specifically, an adapted encoder is employed for effective feature extraction, followed by a node-decoder and a loc-decoder to handle the two sub-tasks, respectively. A k-nearest neighbors subgraph interaction strategy is further introduced to enhance spatial reasoning during location decoding. Furthermore, we customize the REINFORCE algorithm to train UD3RL as a unified model capable of generalizing across different problem sizes and varying neighborhood radius types (i.e., constant and random radii). Experimental results show that UD3RL outperforms conventional methods in both solution quality and runtime, while exhibiting strong generalization across problem scales, spatial distributions, and radius ranges, as well as robustness to dynamic environments. HE close-enough traveling salesman problem (CETSP) is a well-known variant of the classical traveling salesman problem (TSP) that preserves its NP-hard complexity [1].

This study evaluates the performance of Soft Actor Critic (SAC), Greedy Actor Critic (GAC), and Truncated Quantile Critics (TQC) in high-dimensional decision-making tasks using fully observable environments. The focus is on parametrized action (PA) spaces, eliminating the need for recurrent networks, with benchmarks Platform-v0 and Goal-v0 testing discrete actions linked to continuous action-parameter spaces. Hyperparameter optimization was performed with Microsoft NNI, ensuring reproducibility by modifying the codebase for GAC and TQC. Results show that Parameterized Action Greedy Actor-Critic (PAGAC) outperformed other algorithms, achieving the fastest training times and highest returns across benchmarks, completing 5,000 episodes in 41:24 for the Platform game and 24:04 for the Robot Soccer Goal game. Its speed and stability provide clear advantages in complex action spaces. Compared to PASAC and PATQC, PAGAC demonstrated superior efficiency and reliability, making it ideal for tasks requiring rapid convergence and robust performance. Future work could explore hybrid strategies combining entropy-regularization with truncation-based methods to enhance stability and expand investigations into generalizability.

Global optimization of expensive, derivative-free black-box functions requires extreme sample efficiency. While Bayesian optimization (BO) is the current state-of-the-art, its performance hinges on surrogate and acquisition function hyper-parameters that are often hand-tuned and fail to generalize across problem landscapes. We present ZeroShotOpt, a general-purpose, pretrained model for continuous black-box optimization tasks ranging from 2D to 20D. Our approach leverages offline reinforcement learning on large-scale optimization trajectories collected from 12 BO variants. To scale pretraining, we generate millions of synthetic Gaussian process-based functions with diverse landscapes, enabling the model to learn transferable optimization policies. As a result, ZeroShotOpt achieves robust zero-shot generalization on a wide array of unseen benchmarks, matching or surpassing the sample efficiency of leading global optimizers, including BO, while also offering a reusable foundation for future extensions and improvements. Our open-source code, dataset, and model are available at: https://github.com/jamisonmeindl/zeroshotopt

Reinforcement learning (RL) is central to improving reasoning in large language models (LLMs) but typically requires ground-truth rewards. Test-Time Reinforcement Learning (TTRL) removes this need by using majority-vote rewards, but relies on heavy online RL and incurs substantial computational cost. We propose RoiRL: Reasoning with offline iterative Reinforcement Learning, a family of lightweight offline learning alternatives that can target the same regularized optimal policies. Unlike TTRL, RoiRL eliminates the need to maintain a reference model and instead optimizes weighted log-likelihood objectives, enabling stable training with significantly lower memory and compute requirements. Experimental results show that RoiRL trains to 2.5x faster and consistently outperforms TTRL on reasoning benchmarks, establishing a scalable path to self-improving LLMs without labels.

Optimizing discrete diffusion model (DDM) with rewards remains a challenge: the non-autoregressive paradigm makes importance sampling intractable and rollout complex, puzzling reinforcement learning methods such as Group Relative Policy Optimization (GRPO). In this study, we introduce MaskGRPO, the first viable approach to enable scalable multimodal reinforcement learning in discrete diffusion with effective importance sampling and modality-specific adaptations. To this end, we first clarify the theoretical foundation for DDMs, which facilitates building an importance estimator that captures valuable token fluctuation for gradient updates. We then delicately tailored the rollout method for visual sequences, which yields diverse completions and reliable optimization gradients. Upon math reasoning, coding, and visual generation benchmarks, MaskGRPO brings more stable and efficient updates, leading to stronger reasoning performance and better generation quality. This study establishes MaskGRPO as a systematic policy optimization approach and the first practical way for discretized visual diffusion.