Dynamic Reinforcement Learning Systems

• Dynamic RL systems are frameworks that merge classical control, stochastic models, and machine learning to address sequential decision-making in non-stationary environments.
• They employ techniques such as policy iteration, policy gradient, and model-based methods to adapt decision policies through continuous system identification and planning.
• Applications in robotics, streaming, storage optimization, and multi-agent systems demonstrate their practical impact by enhancing performance and safety in dynamic settings.

Dynamic reinforcement learning systems are frameworks and algorithms designed to solve sequential decision-making problems in environments characterized by time-evolving, uncertain, or complex dynamics. These systems unify classical control, stochastic processes, and modern machine learning, focusing on how agents can learn to optimally interact with dynamical systems—either modeled as continuous or discrete stochastic processes—by receiving feedback in the form of rewards and using this feedback to adapt their decision policies. The hallmark of dynamic RL systems is their explicit handling of evolving state transitions, often under non-stationarity, partial observability, or complex system constraints, and their ability to integrate policy optimization, system identification, planning, and value estimation in closed-loop adaptive control scenarios (Yaghmaie et al., 2021).

1. Dynamical System Foundations in Reinforcement Learning

A dynamic RL system is fundamentally built upon a stateful, typically stochastic, dynamical system: $$s_{t+1} = f(s_t,a_t) + \epsilon_t,\qquad r_t = R(s_t,a_t),$$ where $s_t\in\mathbb{S}$ is the system state, $a_t\in\mathbb{A}$ is the action, $\epsilon_t$ denotes process noise, and $r_t$ is the instantaneous reward. In the linear quadratic regime frequently studied in control and RL intersections, this specializes to

$$s_{t+1} = A s_t + B a_t + w_t,\qquad r_t = -\left(s_t^T Q s_t + a_t^T R a_t\right),\quad w_t\sim\mathcal{N}(0,W),$$

with $Q\succeq 0$, $R\succ 0$. Both discrete-action (e.g. CartPole, where $\mathbb{A} = \{+1, -1\}$) and continuous-action/continuous-state systems (linear Gaussian, robotic dynamics) are canonical instantiations (Yaghmaie et al., 2021).

Dynamic RL formalizes learning in these systems as a Markov Decision Process (MDP), where the state space $\mathbb{S}$ and action space $\mathbb{A}$ may be finite or continuous, and system behavior is governed by a transition kernel $P(s'|s,a)$ and a reward function $R(s,a)$. This formalism generalizes across sampled-data systems, continuous-time flows, and sampled-data approximations important in physical and cyber-physical systems (Osinenko et al., 2021, Yaghmaie et al., 2021).

2. Core Solution Methods: Policy Iteration, Policy Gradient, and Model-Based RL

Three main algorithmic paradigms define dynamic RL:

1. Policy Iteration / Dynamic Programming (DP): Focuses on iteratively computing value functions $V^\pi$ and policies $\pi$, using the Bellman expectation and optimality equations. For discrete MDPs, this is realized as alternating policy evaluation and improvement steps—with convergence guarantees in the tabular, finite state-action setting and well-understood behavior in linear-quadratic systems (Yaghmaie et al., 2021).
2. Policy Gradient Methods: Directly parameterize and optimize a stochastic policy $\pi_\theta(a|s)$ via the policy gradient theorem,

$$\nabla_\theta J = \mathbb{E}_{\tau\sim\pi_\theta}\left[R(\tau) \sum_{t=0}^T \nabla_\theta\log \pi_\theta(a_t|s_t)\right].$$

Variance-reduction techniques (e.g., reward-to-go, baselines) and architectural constraints (actor-critic, trust region updates) enable scalability to high-dimensional, continuous-action dynamical systems.

1. Model-Based RL: Simultaneously learns an approximate system model $\hat{f}(s,a)$ and reward $\hat{R}(s,a)$ from trajectory data (system identification via least squares, Gaussian processes), enabling planning via model-predictive control (MPC), synthetic transitions (Dyna-Q), or re-solving optimal control problems (Yaghmaie et al., 2021, Osinenko et al., 2021).

Algorithmic templates (policy iteration, REINFORCE, Dyna-Q) operationalize these approaches across discrete and continuous domains.

3. Advanced Dynamic RL Architectures and Adaptation Mechanisms

Recent research extends dynamic RL systems along multiple axes to enhance adaptivity, safety, and generalization in non-stationary, high-dimensional environments:

• Stacked RL and Hybrid MPC frameworks: These methods, exemplified by "stacked RL" (Osinenko et al., 2021), plan over finite time horizons using a receding-horizon optimization (MPC-style), where the per-stage cost is replaced by critic-estimated $Q$-values and value-to-go terms are learned from data. This yields effective integration of RL with classical MPC, conferring optimality and robust empirical performance in real-time control deployment on physical systems.
• Experience Particle and Reinforcement Field Models: Generalized RL architectures with adaptive, parametric action representations ("action operators"), kernel-based reinforcement fields derived from memory of past state-action-reward tuples ("experience particles"), and memory-graph–based decision abstraction enable online adaptation under changing action semantics and system drift (Chiu et al., 2022).
• Few-Shot System Identification: Leveraging variational inference over latent dynamics parameters, dynamic RL agents can adapt to new or time-varying system instances in a few trajectories by inferring the posterior over $z$ (latent dynamics) and re-planning via MPC in latent space. This approach yields substantial sample efficiency in model-based RL over parametric dynamical system families (Farid et al., 2021).
• Multi-Agent and Decentralized Dynamic Systems: Dynamic RL extends to multi-agent and networked systems with evolving topologies or constraints, using decentralized policy training, attention-based communication, and negotiation protocols to dynamically optimize global objectives (e.g., dynamic communication for MARL routing (McClusky, 2024), negotiation-based RMS scheduling (Sekar et al., 11 Nov 2025)).

4. Theoretical Guarantees: Stability, Convergence, and Optimality

Dynamic RL methods are accompanied by rigorous analyses under specific conditions:

• Policy Iteration Convergence: Finite policy spaces guarantee convergence in finite MDPs. In continuous state or action spaces, approximate DP methods (fitted value iteration, fitted Q-iteration) require structural assumptions (e.g., linearity, convexity) for provable convergence (Yaghmaie et al., 2021).
• Policy Gradient Convergence: Under smoothness and bounded-variance conditions, policy gradient methods converge to local optima. Actor-critic, baseline subtraction, and trust-region schemes improve practical stability.
• Model-Based Consistency and Optimality: For hybrid stack/critic-MPC frameworks, as the sampling period $\delta \to 0$, the solution of the stacked Bellman/MPC problem converges to the true continuous-time optimal control, provided the system and cost are Lipschitz and the action space is compact (Osinenko et al., 2021).
• Safety and Robustness Certificates: Lyapunov-based RL introduces explicit stability criteria for nonlinear stochastic systems with constraints, enforcing Uniformly Ultimate Boundedness (UUB) stability by embedding Lyapunov critics and constraint-regularized updates in both off-policy (LSAC) and on-policy (LCPO) actor-critic frameworks (Han et al., 2020).

5. Applications and Empirical Performance

Dynamic RL systems are deployed across a range of domains:

Domain	Key Example(s)	Performance Highlights
Physical robot control	Mobile robot parking, 6-DoF manipulator (Osinenko et al., 2021, Ota et al., 2019)	RL controllers outperform PID/traditional MPC, achieving smoother, more robust trajectories.
Non-stationary system management	ABR streaming, straggler mitigation (Hamadanian et al., 2022)	Multi-expert dynamic RL achieves up to 2x latency reduction and 30% improved QoE versus single-policy baselines.
Real-time storage optimization	RL-Storage kernel agent (Cheng et al., 2024)	Throughput increased up to 2.6×, latency reduced by 43–50% at negligible resource cost.
Multi-agent decentralized optimization	Dynamic routing, manufacturing scheduling (McClusky, 2024, Sekar et al., 11 Nov 2025)	9.5% higher average rewards, 6.4% less communication, and reduced makespan/tardiness in dynamic environments.

In all scenarios, dynamic RL achieves superiority over static heuristics or conventional single-policy methods by actively adapting to time-varying contexts, inferring and leveraging new information, and managing exploration-exploitation tradeoffs in situ.

6. Challenges and Open Directions

Dynamic RL systems, despite their successes, remain limited by:

• Function approximation and scalability: Generalization in high-dimensional settings depends critically on the stability of nonlinear approximators (deep networks), with instabilities ("deadly triad") arising in off-policy and bootstrap-dominated regimes (Attar et al., 2019).
• Model uncertainty and error propagation: In model-based dynamic RL, compounding model errors can bias planning and degrade performance, motivating robustification (uncertainty penalties, ensemble models) or dynamic model refinement (Yaghmaie et al., 2021, Osinenko et al., 2021).
• Non-stationarity: Abrupt environment shifts challenge standard experience replay and necessitate architectural mechanisms such as multi-expert policies, context detection, or associative memory graphs for retention and transfer across regimes (Hamadanian et al., 2022, Chiu et al., 2022).
• Safety and formal guarantees: Dynamic RL must ensure safety-critical constraints are satisfied during learning and deployment. Shielding and Lyapunov-based RL provide formal methods for safety-aware learning in partially-known or fully model-free settings (Waga et al., 2022, Han et al., 2020).
• Integration with other learning modalities: Future work includes deeper integration with self-supervised learning, causal modeling, advanced representation learning, and extending memory, communication, and abstraction modules for long-horizon, transfer, and autonomous open-ended learning (Chiu et al., 2022).

Dynamic reinforcement learning systems, by combining principled modeling of dynamical processes, advanced policy optimization algorithms, continual system identification, and architectural innovations for adaptation, are central to the next generation of autonomous agents and control systems in time-evolving, uncertain, and safety-critical domains.