Jonas Hübotter

Daniel Widmer, Dongho Kang, Bhavya Sukhija et al.

This paper presents a data-driven strategy to streamline the deployment of model-based controllers in legged robotic hardware platforms. Our approach leverages a model-free safe learning algorithm to automate the tuning of control gains, addressing the mismatch between the simplified model used in the control formulation and the real system. This method substantially mitigates the risk of hazardous interactions with the robot by sample-efficiently optimizing parameters within a probably safe region. Additionally, we extend the applicability of our approach to incorporate the different gait parameters as contexts, leading to a safe, sample-efficient exploration algorithm capable of tuning a motion controller for diverse gait patterns. We validate our method through simulation and hardware experiments, where we demonstrate that the algorithm obtains superior performance on tuning a model-based motion controller for multiple gaits safely.

Jonas Hübotter, Frederike Lübeck, Lejs Behric et al.

Large language models are increasingly post-trained with reinforcement learning in verifiable domains such as code and math. Yet, current methods for reinforcement learning with verifiable rewards (RLVR) learn only from a scalar outcome reward per attempt, creating a severe credit-assignment bottleneck. Many verifiable environments actually provide rich textual feedback, such as runtime errors or judge evaluations, that explain why an attempt failed. We formalize this setting as reinforcement learning with rich feedback and introduce Self-Distillation Policy Optimization (SDPO), which converts tokenized feedback into a dense learning signal without any external teacher or explicit reward model. SDPO treats the current model conditioned on feedback as a self-teacher and distills its feedback-informed next-token predictions back into the policy. In this way, SDPO leverages the model's ability to retrospectively identify its own mistakes in-context. Across scientific reasoning, tool use, and competitive programming on LiveCodeBench v6, SDPO improves sample efficiency and final accuracy over strong RLVR baselines. Notably, SDPO also outperforms baselines in standard RLVR environments that only return scalar feedback by using successful rollouts as implicit feedback for failed attempts. Finally, applying SDPO to individual questions at test time accelerates discovery on difficult binary-reward tasks, achieving the same discovery probability as best-of-k sampling or multi-turn conversations with 3x fewer attempts.

Idan Shenfeld, Mehul Damani, Jonas Hübotter et al.

Continual learning, enabling models to acquire new skills and knowledge without degrading existing capabilities, remains a fundamental challenge for foundation models. While on-policy reinforcement learning can reduce forgetting, it requires explicit reward functions that are often unavailable. Learning from expert demonstrations, the primary alternative, is dominated by supervised fine-tuning (SFT), which is inherently off-policy. We introduce Self-Distillation Fine-Tuning (SDFT), a simple method that enables on-policy learning directly from demonstrations. SDFT leverages in-context learning by using a demonstration-conditioned model as its own teacher, generating on-policy training signals that preserve prior capabilities while acquiring new skills. Across skill learning and knowledge acquisition tasks, SDFT consistently outperforms SFT, achieving higher new-task accuracy while substantially reducing catastrophic forgetting. In sequential learning experiments, SDFT enables a single model to accumulate multiple skills over time without performance regression, establishing on-policy distillation as a practical path to continual learning from demonstrations.

Lenart Treven, Jonas Hübotter, Bhavya Sukhija et al.

Reinforcement learning algorithms typically consider discrete-time dynamics, even though the underlying systems are often continuous in time. In this paper, we introduce a model-based reinforcement learning algorithm that represents continuous-time dynamics using nonlinear ordinary differential equations (ODEs). We capture epistemic uncertainty using well-calibrated probabilistic models, and use the optimistic principle for exploration. Our regret bounds surface the importance of the measurement selection strategy(MSS), since in continuous time we not only must decide how to explore, but also when to observe the underlying system. Our analysis demonstrates that the regret is sublinear when modeling ODEs with Gaussian Processes (GP) for common choices of MSS, such as equidistant sampling. Additionally, we propose an adaptive, data-dependent, practical MSS that, when combined with GP dynamics, also achieves sublinear regret with significantly fewer samples. We showcase the benefits of continuous-time modeling over its discrete-time counterpart, as well as our proposed adaptive MSS over standard baselines, on several applications.

Emre Can Acikgoz, Cheng Qian, Jonas Hübotter et al.

Large language models (LLMs) are becoming the foundation for autonomous agents that can use tools to solve complex tasks. Reinforcement learning (RL) has emerged as a common approach for injecting such agentic capabilities, but typically under tightly controlled training setups. It often depends on carefully constructed task-solution pairs and substantial human supervision, which creates a fundamental obstacle to open-ended self-evolution toward superintelligent systems. In this paper, we propose Tool-R0 framework for training general purpose tool-calling agents from scratch with self-play RL, under a zero-data assumption. Initialized from the same base LLM, Tool-R0 co-evolves a Generator and a Solver with complementary rewards: one proposes targeted challenging tasks at the other's competence frontier and the other learns to solve them with real-world tool calls. This creates a self-evolving cycle that requires no pre-existing tasks or datasets. Evaluation on different tool-use benchmarks show that Tool-R0 yields 92.5 relative improvement over the base model and surpasses fully supervised tool-calling baselines under the same setting. Our work further provides empirical insights into self-play LLM agents by analyzing co-evolution, curriculum dynamics, and scaling behavior.

Jonas Hübotter, Bhavya Sukhija, Lenart Treven et al.

We study a generalization of classical active learning to real-world settings with concrete prediction targets where sampling is restricted to an accessible region of the domain, while prediction targets may lie outside this region. We analyze a family of decision rules that sample adaptively to minimize uncertainty about prediction targets. We are the first to show, under general regularity assumptions, that such decision rules converge uniformly to the smallest possible uncertainty obtainable from the accessible data. We demonstrate their strong sample efficiency in two key applications: active fine-tuning of large neural networks and safe Bayesian optimization, where they achieve state-of-the-art performance.

Tim Launer, Jonas Hübotter, Marco Bagatella et al.

We investigate Functional Majority Voting (FMV), a method based on functional consensus for code generation with Large Language Models, which identifies a representative solution from multiple generations using their runtime execution signatures on test inputs. We find that FMV is an effective test-time inference strategy, substantially boosting performance on LiveCodeBench without a large compute overhead. Furthermore, we extend the utility of functional consensus and apply it as an aggregation strategy for label-free Test-Time Reinforcement Learning. We demonstrate that this increases pass@1 on holdout tasks, but find no evidence of self-improvement beyond the base model's performance ceiling.

Andreas Krause, Jonas Hübotter

Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and driving cars. In recent years, there have been exciting advances in learning-based, data-driven approaches towards AI, and machine learning and deep learning have enabled computer systems to perceive the world in unprecedented ways. Reinforcement learning has enabled breakthroughs in complex games such as Go and challenging robotics tasks such as quadrupedal locomotion. A key aspect of intelligence is to not only make predictions, but reason about the uncertainty in these predictions, and to consider this uncertainty when making decisions. This is what this manuscript on "Probabilistic Artificial Intelligence" is about. The first part covers probabilistic approaches to machine learning. We discuss the differentiation between "epistemic" uncertainty due to lack of data and "aleatoric" uncertainty, which is irreducible and stems, e.g., from noisy observations and outcomes. We discuss concrete approaches towards probabilistic inference and modern approaches to efficient approximate inference. The second part of the manuscript is about taking uncertainty into account in sequential decision tasks. We consider active learning and Bayesian optimization -- approaches that collect data by proposing experiments that are informative for reducing the epistemic uncertainty. We then consider reinforcement learning and modern deep RL approaches that use neural network function approximation. We close by discussing modern approaches in model-based RL, which harness epistemic and aleatoric uncertainty to guide exploration, while also reasoning about safety.

Thomas Kleine Buening, Jonas Hübotter, Barna Pásztor et al.

Multi-turn user interactions are among the most abundant data produced by language models, yet we lack effective methods to learn from them. While typically discarded, these interactions often contain useful information: follow-up user messages may indicate that a response was incorrect, failed to follow an instruction, or did not align with the user's preferences. Importantly, language models are already able to make use of this information in context. After observing a user's follow-up, the same model is often able to revise its behavior. We leverage this ability to propose a principled and scalable method for learning directly from user interactions through self-distillation. By conditioning the model on the user's follow-up message and comparing the resulting token distribution with the original policy, we obtain a target for updating the policy that captures how the model's behavior changes in hindsight. We then distill this hindsight distribution back into the current policy. Remarkably, we show that training on real-world user conversations from WildChat improves language models across standard alignment and instruction-following benchmarks, without regressing other capabilities. The same mechanism enables personalization, allowing models to continually adapt to individual users through interaction without explicit feedback. Our results demonstrate that raw user interactions that arise naturally during deployment enable alignment, personalization, and continual adaptation.

Nicolas Menet, Jonas Hübotter, Parnian Kassraie et al.

We consider the problem of computing the probability of maximality (PoM) of a Gaussian random vector, i.e., the probability for each dimension to be maximal. This is a key challenge in applications ranging from Bayesian optimization to reinforcement learning, where the PoM not only helps with finding an optimal action, but yields a fine-grained analysis of the action domain, crucial in tasks such as drug discovery. Existing techniques are costly, scaling polynomially in computation and memory with the vector size. We introduce LITE, the first approach for estimating Gaussian PoM with almost-linear time and memory complexity. LITE achieves SOTA accuracy on a number of tasks, while being in practice several orders of magnitude faster than the baselines. This also translates to a better performance on downstream tasks such as entropy estimation and optimal control of bandits. Theoretically, we cast LITE as entropy-regularized UCB and connect it to prior PoM estimators.

Jonas Hübotter, Bhavya Sukhija, Lenart Treven et al.

We study the question: How can we select the right data for fine-tuning to a specific task? We call this data selection problem active fine-tuning and show that it is an instance of transductive active learning, a novel generalization of classical active learning. We propose ITL, short for information-based transductive learning, an approach which samples adaptively to maximize information gained about the specified task. We are the first to show, under general regularity assumptions, that such decision rules converge uniformly to the smallest possible uncertainty obtainable from the accessible data. We apply ITL to the few-shot fine-tuning of large neural networks and show that fine-tuning with ITL learns the task with significantly fewer examples than the state-of-the-art.

Matthias Otth, Jonas Hübotter, Ido Hakimi et al.

Recent work has shown that language models can self-improve by maximizing their own confidence in their predictions, without relying on external verifiers or reward signals. In this work, we study the test-time scaling of language models for mathematical reasoning tasks, where the model's own confidence is used to select the most promising attempts. Surprisingly, we find that we can achieve significant performance gains by continuing only the most promising attempt, selected by the model's prefix-confidence. We systematically evaluate prefix-confidence scaling on five mathematical reasoning datasets: the school-level GSM8K and MATH500, and the competition-level AMC23, AIME24, and AIME25. We find that prefix-confidence scaling with prefixes of only 32 tokens achieves a better accuracy-compute trade-off than majority voting. Moreover, prefix-confidence scaling appears less susceptible than BoN to length biases. Finally, we also evaluate test-time training with prefix-confidence and find that, while outperforming the base model, it does not improve over prefix-confidence scaling.

Jonas Hübotter, Leander Diaz-Bone, Ido Hakimi et al.

Humans are good at learning on the job: We learn how to solve the tasks we face as we go along. Can a model do the same? We propose an agent that assembles a task-specific curriculum, called test-time curriculum (TTC-RL), and applies reinforcement learning to continue training the model for its target task. The test-time curriculum avoids time-consuming human curation of datasets by automatically selecting the most task-relevant data from a large pool of available training data. Our experiments demonstrate that reinforcement learning on a test-time curriculum consistently improves the model on its target tasks, across a variety of evaluations and models. Notably, on challenging math and coding benchmarks, TTC-RL improves the pass@1 of Qwen3-8B by approximately 1.8x on AIME25 and 2.1x on CodeElo. Moreover, we find that TTC-RL significantly raises the performance ceiling compared to the initial model, increasing pass@8 on AIME25 from 40% to 62% and on CodeElo from 28% to 43%. Our findings show the potential of test-time curricula in extending the test-time scaling paradigm to continual training on thousands of task-relevant experiences during test-time.