A widely-used actor-critic reinforcement learning algorithm for continuous control, Deep Deterministic Policy Gradients (DDPG), suffers from the overestimation problem, which can negatively affect the performance. Although the state-of-the-art Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm mitigates the overestimation issue, it can lead to a large underestimation bias. In this paper, we propose to use the Boltzmann softmax operator for value function estimation in continuous control. We first theoretically analyze the softmax operator in continuous action space. Then, we uncover an important property of the softmax operator in actor-critic algorithms, i.e., it helps to smooth the optimization landscape, which sheds new light on the benefits of the operator. We also design two new algorithms, Softmax Deep Deterministic Policy Gradients (SD2) and Softmax Deep Double Deterministic Policy Gradients (SD3), by building the softmax operator upon single and double estimators, which can effectively improve the overestimation and underestimation bias. We conduct extensive experiments on challenging continuous control tasks, and results show that SD3 outperforms state-of-the-art methods.

Off-policy model-free deep reinforcement learning methods using previously collected data can improve sample efficiency over on-policy policy gradient techniques. On the other hand, on-policy algorithms are often more stable and easier to use. This paper examines, both theoretically and empirically, approaches to merging on-and off-policy updates for deep reinforcement learning.

In this paper, we propose a second-order deterministic actor-critic framework in reinforcement learning that extends the classical deterministic policy gradient method to exploit curvature information of the performance function. Building on the concept of compatible function approximation for the critic, we introduce a quadratic critic that simultaneously preserves the true policy gradient and an approximation of the performance Hessian. A least-squares temporal difference learning scheme is then developed to estimate the quadratic critic parameters efficiently. This construction enables a quasi-Newton actor update using information learned by the critic, yielding faster convergence compared to first-order methods. The proposed approach is general and applicable to any differentiable policy class. Numerical examples demonstrate that the method achieves improved convergence and performance over standard deterministic actor-critic baselines.

We first theoretically analyze the softmax operator in continuous action space.

Deep Reinforcement Learning (RL) has emerged as a powerful method for addressing complex control problems, particularly those involving underactuated robotic systems. However, in some cases, policies may require refinement to achieve optimal performance and robustness aligned with specific task objectives. In this paper, we propose an approach for fine-tuning Deep RL policies using Evolutionary Strategies (ES) to enhance control performance for underactuated robots. Our method involves initially training an RL agent with Soft-Actor Critic (SAC) using a surrogate reward function designed to approximate complex specific scoring metrics. We subsequently refine this learned policy through a zero-order optimization step employing the Separable Natural Evolution Strategy (SNES), directly targeting the original score. Experimental evaluations conducted in the context of the 2nd AI Olympics with RealAIGym at IROS 2024 demonstrate that our evolutionary fine-tuning significantly improves agent performance while maintaining high robustness. The resulting controllers outperform established baselines, achieving competitive scores for the competition tasks.

Policy gradients methods [1, 3, 4, 6, 7] are now widely used, and have produced impressive empirical results. In continuous control, they have been derived for both stochastic [3] and deterministic [7] policies. The resulting algorithms have different strengths and weaknesses, even though there are a number of similarities in how they are applied in practice, and recent generalizations [10, 13] have pointed to even deeper similarities. Here we study the relationship between the two. First we focus on MDPs with Gaussian control noise and quadratic control cost (while the dynamics and state cost remain general) and show that deterministic and stochastic policy gradients for such MDPs are equivalent. We then develop a much more general result, where any MDP with stochastic policy can be converted into an equivalent MDP with deterministic policy. The new MDP has the same state and policy parameters, but a different control space - namely the sufficient statistics of the stochastic policy in the original MDP. The only quantities that are not equivalent (in either the special or general case) are the state-control value functions. The latter observation suggests that policy gradient methods can be unified by approximating state value functions, instead of the common practice of approximating state-control value functions.

Actor-critic methods, like Twin Delayed Deep Deterministic Policy Gradient (TD3), depend on basic noise-based exploration, which can result in less than optimal policy convergence. In this study, we introduce Monte Carlo Beam Search (MCBS), a new hybrid method that combines beam search and Monte Carlo rollouts with TD3 to improve exploration and action selection. MCBS produces several candidate actions around the policy's output and assesses them through short-horizon rollouts, enabling the agent to make better-informed choices. We test MCBS across various continuous-control benchmarks, including HalfCheetah-v4, Walker2d-v5, and Swimmer-v5, showing enhanced sample efficiency and performance compared to standard TD3 and other baseline methods like SAC, PPO, and A2C. Our findings emphasize MCBS's capability to enhance policy learning through structured look-ahead search while ensuring computational efficiency. Additionally, we offer a detailed analysis of crucial hyperparameters, such as beam width and rollout depth, and explore adaptive strategies to optimize MCBS for complex control tasks. Our method shows a higher convergence rate across different environments compared to TD3, SAC, PPO, and A2C. For instance, we achieved 90% of the maximum achievable reward within around 200 thousand timesteps compared to 400 thousand timesteps for the second-best method.

Practical control systems pose significant challenges in identifying optimal control policies due to uncertainties in the system model and external disturbances. While $H_\infty$ control techniques are commonly used to design robust controllers that mitigate the effects of disturbances, these methods often require complex and computationally intensive calculations. To address this issue, this paper proposes a reinforcement learning algorithm called Robust Deterministic Policy Gradient (RDPG), which formulates the $H_\infty$ control problem as a two-player zero-sum dynamic game. In this formulation, one player (the user) aims to minimize the cost, while the other player (the adversary) seeks to maximize it. We then employ deterministic policy gradient (DPG) and its deep reinforcement learning counterpart to train a robust control policy with effective disturbance attenuation. In particular, for practical implementation, we introduce an algorithm called robust deep deterministic policy gradient (RDDPG), which employs a deep neural network architecture and integrates techniques from the twin-delayed deep deterministic policy gradient (TD3) to enhance stability and learning efficiency. To evaluate the proposed algorithm, we implement it on an unmanned aerial vehicle (UAV) tasked with following a predefined path in a disturbance-prone environment. The experimental results demonstrate that the proposed method outperforms other control approaches in terms of robustness against disturbances, enabling precise real-time tracking of moving targets even under severe disturbance conditions.

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.

Among the many variants of RL, an important class of problems is where the state and action spaces are continuous -- autonomous robots, autonomous vehicles, optimal control are all examples of such problems that can lend themselves naturally to reinforcement based algorithms, and have continuous state and action spaces. In this paper, we introduce a prioritized form of a combination of state-of-the-art approaches such as Deep Q-learning (DQN) and Deep Deterministic Policy Gradient (DDPG) to outperform the earlier results for continuous state and action space problems. Our experiments also involve the use of parameter noise during training resulting in more robust deep RL models outperforming the earlier results significantly. We believe these results are a valuable addition for continuous state and action space problems.