Lenart Treven

Bhavya Sukhija, Lenart Treven, Cansu Sancaktar et al.

Reinforcement learning algorithms commonly seek to optimize policies for solving one particular task. How should we explore an unknown dynamical system such that the estimated model globally approximates the dynamics and allows us to solve multiple downstream tasks in a zero-shot manner? In this paper, we address this challenge, by developing an algorithm -- OPAX -- for active exploration. OPAX uses well-calibrated probabilistic models to quantify the epistemic uncertainty about the unknown dynamics. It optimistically -- w.r.t. to plausible dynamics -- maximizes the information gain between the unknown dynamics and state observations. We show how the resulting optimization problem can be reduced to an optimal control problem that can be solved at each episode using standard approaches. We analyze our algorithm for general models, and, in the case of Gaussian process dynamics, we give a first-of-its-kind sample complexity bound and show that the epistemic uncertainty converges to zero. In our experiments, we compare OPAX with other heuristic active exploration approaches on several environments. Our experiments show that OPAX is not only theoretically sound but also performs well for zero-shot planning on novel downstream tasks.

Marcell Bartos, Bruce D. Lee, Lenart Treven et al.

Optimism in the face of uncertainty is a popular approach to balance exploration and exploitation in reinforcement learning. Here, we consider the online linear quadratic regulator (LQR) problem, i.e., to learn the LQR corresponding to an unknown linear dynamical system by adapting the control policy online based on closed-loop data collected during operation. In this work, we propose Intrinsic Rewards LQR (IR-LQR), an optimistic online LQR algorithm that applies the idea of intrinsic rewards originating from reinforcement learning and the concept of variance regularization to promote uncertainty-driven exploration. IR-LQR retains the structure of a standard LQR synthesis problem by only modifying the cost function, resulting in an intuitively pleasing, simple, computationally cheap, and efficient algorithm. This is in contrast to existing optimistic online LQR formulations that rely on more complicated iterative search algorithms or solve computationally demanding optimization problems. We show that IR-LQR achieves the optimal worst-case regret rate of $\sqrt{T}$, and compare it to various state-of-the-art online LQR algorithms via numerical experiments carried out on an aircraft pitch angle control and an unmanned aerial vehicle example.

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.

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.

Yarden As, Bhavya Sukhija, Lenart Treven et al.

Reinforcement learning (RL) is ubiquitous in the development of modern AI systems. However, state-of-the-art RL agents require extensive, and potentially unsafe, interactions with their environments to learn effectively. These limitations confine RL agents to simulated environments, hindering their ability to learn directly in real-world settings. In this work, we present ActSafe, a novel model-based RL algorithm for safe and efficient exploration. ActSafe learns a well-calibrated probabilistic model of the system and plans optimistically w.r.t. the epistemic uncertainty about the unknown dynamics, while enforcing pessimism w.r.t. the safety constraints. Under regularity assumptions on the constraints and dynamics, we show that ActSafe guarantees safety during learning while also obtaining a near-optimal policy in finite time. In addition, we propose a practical variant of ActSafe that builds on latest model-based RL advancements and enables safe exploration even in high-dimensional settings such as visual control. We empirically show that ActSafe obtains state-of-the-art performance in difficult exploration tasks on standard safe deep RL benchmarks while ensuring safety during learning.

Jonas Rothfuss, Bhavya Sukhija, Lenart Treven et al.

We present SIM-FSVGD for learning robot dynamics from data. As opposed to traditional methods, SIM-FSVGD leverages low-fidelity physical priors, e.g., in the form of simulators, to regularize the training of neural network models. While learning accurate dynamics already in the low data regime, SIM-FSVGD scales and excels also when more data is available. We empirically show that learning with implicit physical priors results in accurate mean model estimation as well as precise uncertainty quantification. We demonstrate the effectiveness of SIM-FSVGD in bridging the sim-to-real gap on a high-performance RC racecar system. Using model-based RL, we demonstrate a highly dynamic parking maneuver with drifting, using less than half the data compared to the state of the art.

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.

Klemens Iten, Lenart Treven, Bhavya Sukhija et al.

Reinforcement learning algorithms are typically designed for discrete-time dynamics, even though the underlying real-world control systems are often continuous in time. In this paper, we study the problem of continuous-time reinforcement learning, where the unknown system dynamics are represented using nonlinear ordinary differential equations (ODEs). We leverage probabilistic models, such as Gaussian processes and Bayesian neural networks, to learn an uncertainty-aware model of the underlying ODE. Our algorithm, COMBRL, greedily maximizes a weighted sum of the extrinsic reward and model epistemic uncertainty. This yields a scalable and sample-efficient approach to continuous-time model-based RL. We show that COMBRL achieves sublinear regret in the reward-driven setting, and in the unsupervised RL setting (i.e., without extrinsic rewards), we provide a sample complexity bound. In our experiments, we evaluate COMBRL in both standard and unsupervised RL settings and demonstrate that it scales better, is more sample-efficient than prior methods, and outperforms baselines across several deep RL tasks.

Klemens Iten, Bruce Lee, Chenhao Li et al.

Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under time-varying dynamics. We consider a continual model-based reinforcement learning setting in which an agent repeatedly learns and controls a dynamical system whose transition dynamics evolve across episodes. We analyze the problem using Gaussian process dynamics models under frequentist variation-budget assumptions. Our analysis shows that persistent non-stationarity requires explicitly limiting the influence of outdated data to maintain calibrated uncertainty and meaningful dynamic regret guarantees. Motivated by these insights, we propose a practical optimistic model-based reinforcement learning algorithm with adaptive data buffer mechanisms and demonstrate improved performance on continuous control benchmarks with non-stationary dynamics.

Bhavya Sukhija, Lenart Treven, Carmelo Sferrazza et al.

We address the challenge of efficient exploration in model-based reinforcement learning (MBRL), where the system dynamics are unknown and the RL agent must learn directly from online interactions. We propose Scalable and Optimistic MBRL (SOMBRL), an approach based on the principle of optimism in the face of uncertainty. SOMBRL learns an uncertainty-aware dynamics model and greedily maximizes a weighted sum of the extrinsic reward and the agent's epistemic uncertainty. SOMBRL is compatible with any policy optimizers or planners, and under common regularity assumptions on the system, we show that SOMBRL has sublinear regret for nonlinear dynamics in the (i) finite-horizon, (ii) discounted infinite-horizon, and (iii) non-episodic settings. Additionally, SOMBRL offers a flexible and scalable solution for principled exploration. We evaluate SOMBRL on state-based and visual-control environments, where it displays strong performance across all tasks and baselines. We also evaluate SOMBRL on a dynamic RC car hardware and show SOMBRL outperforms the state-of-the-art, illustrating the benefits of principled exploration for MBRL.

Arnav Sukhija, Lenart Treven, Jin Cheng et al.

Fixed-frequency control in robotics imposes a trade-off between the efficiency of low-frequency control and the robustness of high-frequency control, a limitation not seen in adaptable biological systems. We address this with a reinforcement learning approach in which policies jointly select control actions and their application durations, enabling robots to autonomously modulate their control frequency in response to situational demands. We validate our method with zero-shot sim-to-real experiments on two distinct hardware platforms: a high-speed RC car and a quadrupedal robot. Our method matches or outperforms fixed-frequency baselines in terms of rewards while significantly reducing the control frequency and exhibiting adaptive frequency control under real-world conditions.

Lenart Treven, Bhavya Sukhija, Jonas Rothfuss et al.

How do we enable AI systems to efficiently learn in the real-world? First-principles models are widely used to simulate natural systems, but often fail to capture real-world complexity due to simplifying assumptions. In contrast, deep learning approaches can estimate complex dynamics with minimal assumptions but require large, representative datasets. We propose SimPEL, a method that efficiently combines first-principles models with data-driven learning by using low-fidelity simulators as priors in Bayesian deep learning. This enables SimPEL to benefit from simulator knowledge in low-data regimes and leverage deep learning's flexibility when more data is available, all the while carefully quantifying epistemic uncertainty. We evaluate SimPEL on diverse systems, including biological, agricultural, and robotic domains, showing superior performance in learning complex dynamics. For decision-making, we demonstrate that SimPEL bridges the sim-to-real gap in model-based reinforcement learning. On a high-speed RC car task, SimPEL learns a highly dynamic parking maneuver involving drifting with substantially less data than state-of-the-art baselines. These results highlight the potential of SimPEL for data-efficient learning and control in complex real-world environments.

Bhavya Sukhija, Lenart Treven, Florian Dörfler et al.

We study the problem of nonepisodic reinforcement learning (RL) for nonlinear dynamical systems, where the system dynamics are unknown and the RL agent has to learn from a single trajectory, i.e., without resets. We propose Nonepisodic Optimistic RL (NeoRL), an approach based on the principle of optimism in the face of uncertainty. NeoRL uses well-calibrated probabilistic models and plans optimistically w.r.t. the epistemic uncertainty about the unknown dynamics. Under continuity and bounded energy assumptions on the system, we provide a first-of-its-kind regret bound of $O(Γ_T \sqrt{T})$ for general nonlinear systems with Gaussian process dynamics. We compare NeoRL to other baselines on several deep RL environments and empirically demonstrate that NeoRL achieves the optimal average cost while incurring the least regret.

Lenart Treven, Bhavya Sukhija, Yarden As et al.

Reinforcement learning (RL) excels in optimizing policies for discrete-time Markov decision processes (MDP). However, various systems are inherently continuous in time, making discrete-time MDPs an inexact modeling choice. In many applications, such as greenhouse control or medical treatments, each interaction (measurement or switching of action) involves manual intervention and thus is inherently costly. Therefore, we generally prefer a time-adaptive approach with fewer interactions with the system. In this work, we formalize an RL framework, Time-adaptive Control & Sensing (TaCoS), that tackles this challenge by optimizing over policies that besides control predict the duration of its application. Our formulation results in an extended MDP that any standard RL algorithm can solve. We demonstrate that state-of-the-art RL algorithms trained on TaCoS drastically reduce the interaction amount over their discrete-time counterpart while retaining the same or improved performance, and exhibiting robustness over discretization frequency. Finally, we propose OTaCoS, an efficient model-based algorithm for our setting. We show that OTaCoS enjoys sublinear regret for systems with sufficiently smooth dynamics and empirically results in further sample-efficiency gains.

Lenart Treven, Philippe Wenk, Florian Dörfler et al.

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the adjoint method, many downstream tasks such as active learning, exploration in reinforcement learning, robust control, or filtering require accurate estimates of predictive uncertainties. In this work, we propose a novel approach towards estimating epistemically uncertain neural ODEs, avoiding the numerical integration bottleneck. Instead of modeling uncertainty in the ODE parameters, we directly model uncertainties in the state space. Our algorithm - distributional gradient matching (DGM) - jointly trains a smoother and a dynamics model and matches their gradients via minimizing a Wasserstein loss. Our experiments show that, compared to traditional approximate inference methods based on numerical integration, our approach is faster to train, faster at predicting previously unseen trajectories, and in the context of neural ODEs, significantly more accurate.

Luka Kolar, Rok Šikonja, Lenart Treven

We present a novel method for inferring ground-truth signal from multiple degraded signals, affected by different amounts of sensor exposure. The algorithm learns a multiplicative degradation effect by performing iterative corrections of two signals solely from the ratio between them. The degradation function d should be continuous, satisfy monotonicity, and d(0) = 1. We use smoothed monotonic regression method, where we easily incorporate the aforementioned criteria to the fitting part. We include theoretical analysis and prove convergence to the ground-truth signal for the noiseless measurement model. Lastly, we present an approach to fuse the noisy corrected signals using Gaussian processes. We use sparse Gaussian processes that can be utilized for a large number of measurements together with a specialized kernel that enables the estimation of noise values of all sensors. The data fusion framework naturally handles data gaps and provides a simple and powerful method for observing the signal trends on multiple timescales(long-term and short-term signal properties). The viability of correction method is evaluated on a synthetic dataset with known ground-truth signal.

Lenart Treven, Sebastian Curi, Mojmir Mutny et al.

The principal task to control dynamical systems is to ensure their stability. When the system is unknown, robust approaches are promising since they aim to stabilize a large set of plausible systems simultaneously. We study linear controllers under quadratic costs model also known as linear quadratic regulators (LQR). We present two different semi-definite programs (SDP) which results in a controller that stabilizes all systems within an ellipsoid uncertainty set. We further show that the feasibility conditions of the proposed SDPs are \emph{equivalent}. Using the derived robust controller syntheses, we propose an efficient data dependent algorithm -- \textsc{eXploration} -- that with high probability quickly identifies a stabilizing controller. Our approach can be used to initialize existing algorithms that require a stabilizing controller as an input while adding constant to the regret. We further propose different heuristics which empirically reduce the number of steps taken by \textsc{eXploration} and reduce the suffered cost while searching for a stabilizing controller.