Studying the set of exact solutions of a system of polynomial equations largely depends on a single iterative algorithm, known as Buchberger's algorithm. Optimized versions of this algorithm are crucial for many computer algebra systems (e.g., Mathematica, Maple, Sage). We introduce a new approach to Buchberger's algorithm that uses reinforcement learning agents to perform S-pair selection, a key step in the algorithm. We then study how the difficulty of the problem depends on the choices of domain and distribution of polynomials, about which little is known. Finally, we train a policy model using proximal policy optimization (PPO) to learn S-pair selection strategies for random systems of binomial equations. In certain domains, the trained model outperforms state-of-the-art selection heuristics in total number of polynomial additions performed, which provides a proof-of-concept that recent developments in machine learning have the potential to improve performance of algorithms in symbolic computation.

This is the second post devoted to Deep Q-Network (DQN), in the "Deep Reinforcement Learning Explained" series, in which we will analyse some challenges that appear when we apply Deep Learning to Reinforcement Learning. We will also present in detail the code that solves the OpenAI Gym Pong game using the DQN network introduced in the previous post. Unfortunately, reinforcement learning is more unstable when neural networks are used to represent the action-values, despite applying the wrappers introduced in the previous section. Training such a network requires a lot of data, but even then, it is not guaranteed to converge on the optimal value function. In fact, there are situations where the network weights can oscillate or diverge, due to the high correlation between actions and states.

In reinforcement learning, wrappers are universally used to transform the information that passes between a model and an environment. Despite their ubiquity, no library exists with reasonable implementations of all popular preprocessing methods. This leads to unnecessary bugs, code inefficiencies, and wasted developer time. Accordingly we introduce SuperSuit, a Python library that includes all popular wrappers, and wrappers that can easily apply lambda functions to the observations/actions/reward.

Deep Q-Networks (DQN) is one of the most well-known methods of deep reinforcement learning, which uses deep learning to approximate the action-value function. Solving numerous Deep reinforcement learning challenges such as moving targets problem and the correlation between samples are the main advantages of this model. Although there have been various extensions of DQN in recent years, they all use a similar method to DQN to overcome the problem of moving targets. Despite the advantages mentioned, synchronizing the network weight in a fixed step size, independent of the agent's behavior, may in some cases cause the loss of some properly learned networks. These lost networks may lead to states with more rewards, hence better samples stored in the replay memory for future training. In this paper, we address this problem from the DQN family and provide an adaptive approach for the synchronization of the neural weights used in DQN. In this method, the synchronization of weights is done based on the recent behavior of the agent, which is measured by a criterion at the end of the intervals. To test this method, we adjusted the DQN and rainbow methods with the proposed adaptive synchronization method. We compared these adjusted methods with their standard form on well-known games, which results confirm the quality of our synchronization methods.

We present a holistic data-driven approach to the problem of productivity increase on the example of a metallurgical pickling line. The proposed approach combines mathematical modeling as a base algorithm and a cooperative Multi-Agent Reinforcement Learning (MARL) system implemented such as to enhance the performance by multiple criteria while also meeting safety and reliability requirements and taking into account the unexpected volatility of certain technological processes. We demonstrate how Deep Q-Learning can be applied to a real-life task in a heavy industry, resulting in significant improvement of previously existing automation systems.The problem of input data scarcity is solved by a two-step combination of LSTM and CGAN, which helps to embrace both the tabular representation of the data and its sequential properties. Offline RL training, a necessity in this setting, has become possible through the sophisticated probabilistic kinematic environment.

Reinforcement learning is a powerful tool to learn the optimal policy of possibly multiple agents by interacting with the environment. As the number of agents grow to be very large, the system can be approximated by a mean-field problem. Therefore, it has motivated new research directions for mean-field control (MFC) and mean-field game (MFG). In this paper, we study the policy gradient method for the linear-quadratic mean-field control and game, where we assume each agent has identical linear state transitions and quadratic cost functions. While most of the recent works on policy gradient for MFC and MFG are based on discrete-time models, we focus on the continuous-time models where some analyzing techniques can be interesting to the readers. For both MFC and MFG, we provide policy gradient update and show that it converges to the optimal solution at a linear rate, which is verified by a synthetic simulation. For MFG, we also provide sufficient conditions for the existence and uniqueness of the Nash equilibrium.

Reinforcement learning (RL) has received a massive boost in attention recently. Thanks to impressive projects such as DeepMind's AlphaGo and AlphaGo Zero, which beat the world's best players in the strategy board game "Go", RL has garnered extensive news coverage. Just recently, RL was used to compete with the world's top e-sports players in the real-time strategy video game StarCraft II. Python Machine Learning, Third Edition covers the essential concepts of RL, starting from its foundations, and how RL can support decision making in complex environments. The book discusses agent-environment interactions and Markov decision processes (MDP), and considers three main approaches for solving RL problems: dynamic programming, MC learning, and TD learning. It discusses how the dynamic programming algorithm assumes that the full knowledge of environment dynamics is available, an assumption that is not typically true for most real-world problems.

Autonomous Braking and Throttle control is key in developing safe driving systems for the future. There exists a need for autonomous vehicles to negotiate a multi-agent environment while ensuring safety and comfort. A Deep Reinforcement Learning based autonomous throttle and braking system is presented. For each time step, the proposed system makes a decision to apply the brake or throttle. The throttle and brake are modelled as continuous action space values. We demonstrate 2 scenarios where there is a need for a sophisticated braking and throttle system, i.e when there is a static obstacle in front of our agent like a car, stop sign. The second scenario consists of 2 vehicles approaching an intersection. The policies for brake and throttle control are learned through computer simulation using Deep deterministic policy gradients. The experiment shows that the system not only avoids a collision, but also it ensures that there is smooth change in the values of throttle/brake as it gets out of the emergency situation and abides by the speed regulations, i.e the system resembles human driving.

Temporal difference (TD) learning is one of the main foundations of modern reinforcement learning. This paper studies the use of TD(0), a canonical TD algorithm, to estimate the value function of a given policy from a batch of data. In this batch setting, we show that TD(0) may converge to an inaccurate value function because the update following an action is weighted according to the number of times that action occurred in the batch -- not the true probability of the action under the given policy. To address this limitation, we introduce \textit{policy sampling error corrected}-TD(0) (PSEC-TD(0)). PSEC-TD(0) first estimates the empirical distribution of actions in each state in the batch and then uses importance sampling to correct for the mismatch between the empirical weighting and the correct weighting for updates following each action. We refine the concept of a certainty-equivalence estimate and argue that PSEC-TD(0) is a more data efficient estimator than TD(0) for a fixed batch of data. Finally, we conduct an empirical evaluation of PSEC-TD(0) on three batch value function learning tasks, with a hyperparameter sensitivity analysis, and show that PSEC-TD(0) produces value function estimates with lower mean squared error than TD(0).

We consider off-policy evaluation (OPE), which evaluates the performance of a new policy from observed data collected from previous experiments, without requiring the execution of the new policy. This finds important applications in areas with high execution cost or safety concerns, such as medical diagnosis, recommendation systems and robotics. In practice, due to the limited information from off-policy data, it is highly desirable to construct rigorous confidence intervals, not just point estimation, for the policy performance. In this work, we propose a new variational framework which reduces the problem of calculating tight confidence bounds in OPE into an optimization problem on a feasible set that catches the true state-action value function with high probability. The feasible set is constructed by leveraging statistical properties of a recently proposed kernel Bellman loss (Feng et al., 2019). We design an efficient computational approach for calculating our bounds, and extend it to perform post-hoc diagnosis and correction for existing estimators. Empirical results show that our method yields tight confidence intervals in different settings.