arXiv subjects

Grigory Yaremenko

Publications and source records attributed to Grigory Yaremenko.

11 recordsLinked to original sources

arXiv2025

Some remarks on stochastic converse Lyapunov theorems

In this brief note, we investigate some constructions of Lyapunov functions for stochastic discrete-time stabilizable dynamical systems, in other words, controlled Markov chains. The main question here is whether a Lyapunov function in some statistical sense exists if the respective controlled Markov chain admits a stabilizing policy. We demonstrate some constructions extending on the classical results for deterministic systems. Some limitations of the constructed Lyapunov functions for stabilization are discussed, particularly for stabilization in mean. Although results for deterministic systems are well known, the stochastic case was addressed in less detail, which the current paper remarks on. A distinguishable feature of this work is the study of stabilizers that possess computationally tractable convergence certificates.

math.DS↗

arXiv2025

Multi-CALF: A Policy Combination Approach with Statistical Guarantees

We introduce Multi-CALF, an algorithm that intelligently combines reinforcement learning policies based on their relative value improvements. Our approach integrates a standard RL policy with a theoretically-backed alternative policy, inheriting formal stability guarantees while often achieving better performance than either policy individually. We prove that our combined policy converges to a specified goal set with known probability and provide precise bounds on maximum deviation and convergence time. Empirical validation on control tasks demonstrates enhanced performance while maintaining stability guarantees.

cs.LG↗

arXiv2025

A universal policy wrapper with guarantees

We introduce a universal policy wrapper for reinforcement learning agents that ensures formal goal-reaching guarantees. In contrast to standard reinforcement learning algorithms that excel in performance but lack rigorous safety assurances, our wrapper selectively switches between a high-performing base policy -- derived from any existing RL method -- and a fallback policy with known convergence properties. Base policy's value function supervises this switching process, determining when the fallback policy should override the base policy to ensure the system remains on a stable path. The analysis proves that our wrapper inherits the fallback policy's goal-reaching guarantees while preserving or improving upon the performance of the base policy. Notably, it operates without needing additional system knowledge or online constrained optimization, making it readily deployable across diverse reinforcement learning architectures and tasks.

cs.LG↗

arXiv2024

A novel agent with formal goal-reaching guarantees: an experimental study with a mobile robot

Reinforcement Learning (RL) has been shown to be effective and convenient for a number of tasks in robotics. However, it requires the exploration of a sufficiently large number of state-action pairs, many of which may be unsafe or unimportant. For instance, online model-free learning can be hazardous and inefficient in the absence of guarantees that a certain set of desired states will be reached during an episode. An increasingly common approach to address safety involves the addition of a shielding system that constrains the RL actions to a safe set of actions. In turn, a difficulty for such frameworks is how to effectively couple RL with the shielding system to make sure the exploration is not excessively restricted. This work presents a novel safe model-free RL agent called Critic As Lyapunov Function (CALF) and showcases how CALF can be used to improve upon control baselines in robotics in an efficient and convenient fashion while ensuring guarantees of stable goal reaching. The latter is a crucial part of safety, as seen generally. With CALF all state-action pairs remain explorable and yet reaching of desired goal states is formally guaranteed. Formal analysis is provided that shows the goal stabilization-ensuring properties of CALF and a set of real-world and numerical experiments with a non-holonomic wheeled mobile robot (WMR) TurtleBot3 Burger confirmed the superiority of CALF over such a well-established RL agent as proximal policy optimization (PPO), and a modified version of SARSA in a few-episode setting in terms of attained total cost.

cs.RO↗

arXiv2024

Critic as Lyapunov function (CALF): a model-free, stability-ensuring agent

This work presents and showcases a novel reinforcement learning agent called Critic As Lyapunov Function (CALF) which is model-free and ensures online environment, in other words, dynamical system stabilization. Online means that in each learning episode, the said environment is stabilized. This, as demonstrated in a case study with a mobile robot simulator, greatly improves the overall learning performance. The base actor-critic scheme of CALF is analogous to SARSA. The latter did not show any success in reaching the target in our studies. However, a modified version thereof, called SARSA-m here, did succeed in some learning scenarios. Still, CALF greatly outperformed the said approach. CALF was also demonstrated to improve a nominal stabilizer provided to it. In summary, the presented agent may be considered a viable approach to fusing classical control with reinforcement learning. Its concurrent approaches are mostly either offline or model-based, like, for instance, those that fuse model-predictive control into the agent.

cs.RO↗

arXiv2024

An agent design with goal reaching guarantees for enhancement of learning

Reinforcement learning is commonly concerned with problems of maximizing accumulated rewards in Markov decision processes. Oftentimes, a certain goal state or a subset of the state space attain maximal reward. In such a case, the environment may be considered solved when the goal is reached. Whereas numerous techniques, learning or non-learning based, exist for solving environments, doing so optimally is the biggest challenge. Say, one may choose a reward rate which penalizes the action effort. Reinforcement learning is currently among the most actively developed frameworks for solving environments optimally by virtue of maximizing accumulated reward, in other words, returns. Yet, tuning agents is a notoriously hard task as reported in a series of works. Our aim here is to help the agent learn a near-optimal policy efficiently while ensuring a goal reaching property of some basis policy that merely solves the environment. We suggest an algorithm, which is fairly flexible, and can be used to augment practically any agent as long as it comprises of a critic. A formal proof of a goal reaching property is provided. Comparative experiments on several problems under popular baseline agents provided an empirical evidence that the learning can indeed be boosted while ensuring goal reaching property.

cs.AI↗

arXiv2022

A generalized stacked reinforcement learning method for sampled systems

A common setting of reinforcement learning (RL) is a Markov decision process (MDP) in which the environment is a stochastic discrete-time dynamical system. Whereas MDPs are suitable in such applications as video-games or puzzles, physical systems are time-continuous. A general variant of RL is of digital format, where updates of the value (or cost) and policy are performed at discrete moments in time. The agent-environment loop then amounts to a sampled system, whereby sample-and-hold is a specific case. In this paper, we propose and benchmark two RL methods suitable for sampled systems. Specifically, we hybridize model-predictive control (MPC) with critics learning the optimal Q- and value (or cost-to-go) function. Optimality is analyzed and performance comparison is done in an experimental case study with a mobile robot.

cs.RO↗

arXiv2022

A framework for online, stabilizing reinforcement learning

Online reinforcement learning is concerned with training an agent on-the-fly via dynamic interaction with the environment. Here, due to the specifics of the application, it is not generally possible to perform long pre-training, as it is commonly done in off-line, model-free approaches, which are akin to dynamic programming. Such applications may be found more frequently in industry, rather than in pure digital fields, such as cloud services, video games, database management, etc., where reinforcement learning has been demonstrating success. Online reinforcement learning, in contrast, is more akin to classical control, which utilizes some model knowledge about the environment. Stability of the closed-loop (agent plus the environment) is a major challenge for such online approaches. In this paper, we tackle this problem by a special fusion of online reinforcement learning with elements of classical control, namely, based on the Lyapunov theory of stability. The idea is to start the agent at once, without pre-training, and learn approximately optimal policy under specially designed constraints, which guarantee stability. The resulting approach was tested in an extensive experimental study with a mobile robot. A nominal parking controller was used as a baseline. It was observed that the suggested agent could always successfully park the robot, while significantly improving the cost. While many approaches may be exploited for mobile robot control, we suggest that the experiments showed the promising potential of online reinforcement learning agents based on Lyapunov-like constraints. The presented methodology may be utilized in safety-critical, industrial applications where stability is necessary.

eess.SY↗

arXiv2022

On stochastic stabilization via non-smooth control Lyapunov functions

Control Lyapunov function is a central tool in stabilization. It generalizes an abstract energy function -- a Lyapunov function -- to the case of controlled systems. It is a known fact that most control Lyapunov functions are non-smooth -- so is the case in non-holonomic systems, like wheeled robots and cars. Frameworks for stabilization using non-smooth control Lyapunov functions exist, like Dini aiming and steepest descent. This work generalizes the related results to the stochastic case. As the groundwork, sampled control scheme is chosen in which control actions are computed at discrete moments in time using discrete measurements of the system state. In such a setup, special attention should be paid to the sample-to-sample behavior of the control Lyapunov function. A particular challenge here is a random noise acting on the system. The central result of this work is a theorem that states, roughly, that if there is a, generally non-smooth, control Lyapunov function, the given stochastic dynamical system can be practically stabilized in the sample-and-hold mode meaning that the control actions are held constant within sampling time steps. A particular control method chosen is based on Moreau-Yosida regularization, in other words, inf-convolution of the control Lyapunov function, but the overall framework is extendable to further control schemes. It is assumed that the system noise be bounded almost surely, although the case of unbounded noise is briefly addressed.

math.OC↗

arXiv2022

On stochastic stabilization of sampled systems

This paper addresses stochastic stabilization in case where implementation of control policies is digital, i. e., when the dynamical system is treated continuous, whereas the control actions are held constant in predefined time steps. In such a setup, special attention should be paid to the sample-to-sample behavior of the involved Lyapunov function. This paper extends on the stochastic stability results specifically to address for the sample-and-hold mode. We show that if a Markov policy stabilizes the system in a suitable sense, then it also practically stabilizes it in the sample-and-hold sense. This establishes a bridge from an idealized continuous application of the policy to its digital implementation. The central result applies to dynamical systems described by stochastic differential equations driven by the standard Brownian motion. Generalizations are discussed, including the case of non-smooth Lyapunov functions for systems driven by bounded noise. A brief overview of bounded noise models is given.

math.DS↗

arXiv2022

A note on stabilizing reinforcement learning

Reinforcement learning is a general methodology of adaptive optimal control that has attracted much attention in various fields ranging from video game industry to robot manipulators. Despite its remarkable performance demonstrations, plain reinforcement learning controllers do not guarantee stability which compromises their applicability in industry. To provide such guarantees, measures have to be taken. This gives rise to what could generally be called stabilizing reinforcement learning. Concrete approaches range from employment of human overseers to filter out unsafe actions to formally verified shields and fusion with classical stabilizing controllers. A line of attack that utilizes elements of adaptive control has become fairly popular in the recent years. In this note, we critically address such an approach in a fairly general actor-critic setup for nonlinear time-continuous environments. The actor network utilizes a so-called robustifying term that is supposed to compensate for the neural network errors. The corresponding stability analysis is based on the value function itself. We indicate a problem in such a stability analysis and provide a counterexample to the overall control scheme. Implications for such a line of attack in stabilizing reinforcement learning are discussed. Furthermore, unfortunately the said problem possess no fix without a substantial reconsideration of the whole approach. As a positive message, we derive a stochastic critic neural network weight convergence analysis provided that the environment was stabilized.

math.DS↗