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The general problem of quantum compiling is to approximate any unitary transformation that describes the quantum computation as a sequence of elements selected from a finite base of universal quantum gates. The Solovay-Kitaev theorem guarantees the existence of such an approximating sequence. Though, the solutions to the quantum compiling problem suffer from a tradeoff between the length of the sequences, the precompilation time, and the execution time. Traditional approaches are time-consuming, unsuitable to be employed during computation. Here, we propose a deep reinforcement learning method as an alternative strategy, which requires a single precompilation procedure to learn a general strategy to approximate single-qubit unitaries. We show that this approach reduces the overall execution time, improving the tradeoff between the length of the sequence and execution time, potentially allowing real-time operations. Quantum compilers are characterized by a trade-off between the length of the sequences, the precompilation time, and the execution time. Here, the authors propose an approach based on deep reinforcement learning to approximate unitary operators as circuits, and show that this approach decreases the execution time, potentially allowing real-time quantum compiling.

Some problems in physics can be handled only after a suitable ansatz solution has been guessed, proving to be resilient to generalization. The coherent transport of a quantum state by adiabatic passage through an array of semiconductor quantum dots is an excellent example of such a problem, where it is necessary to introduce a so-called counterintuitive control sequence. Instead, the deep reinforcement learning (DRL) technique has proven to be able to solve very complex sequential decision-making problems, despite a lack of prior knowledge. We show that DRL discovers a control sequence that outperforms the counterintuitive control sequence. DRL can even discover novel strategies when realistic disturbances affect an ideal system, such as detuning or when dephasing or losses are added to the master equation. DRL is effective in controlling the dynamics of quantum states and, more generally, whenever an ansatz solution is unknown or insufficient to effectively treat the problem. Many problems in physics do not have an exact solution method, so their resolution has been sometimes possible only by guessing test functions. The authors apply Deep Reinforcement Learning (DRL) to control coherent transport of quantum states in arrays of quantum dots and demonstrate that DRL can solve the control problem in the absence of a known analytical solution even under disturbance conditions.

In real-world applications, inferring the intentions of expert agents (e.g., human operators) can be fundamental to understand how possibly conflicting objectives are managed, helping to interpret the demonstrated behavior. In this paper, we discuss how inverse reinforcement learning (IRL) can be employed to retrieve the reward function implicitly optimized by expert agents acting in real applications. Scaling IRL to real-world cases has proved challenging as typically only a fixed dataset of demonstrations is available and further interactions with the environment are not allowed. For this reason, we resort to a class of truly batch model-free IRL algorithms and we present three application scenarios: (1) the high-level decision-making problem in the highway driving scenario, and (2) inferring the user preferences in a social network (Twitter), and (3) the management of the water release in the Como Lake. For each of these scenarios, we provide formalization, experiments and a discussion to interpret the obtained results.

This paper is about the exploitation of Lipschitz continuity properties for Markov Decision Processes to safely speed up policy-gradient algorithms. Starting from assumptions about the Lipschitz continuity of the state-transition model, the reward function, and the policies considered in the learning process, we show that both the expected return of a policy and its gradient are Lipschitz continuous w.r.t. policy parameters. By leveraging such properties, we define policy-parameter updates that guarantee a performance improvement at each iteration. The proposed methods are empirically evaluated and compared to other related approaches using different configurations of three popular control scenarios: the linear quadratic regulator, the mass-spring-damper system and the ship-steering control.

Policy gradient (PG) algorithms are among the best candidates for the much-anticipated applications of reinforcement learning to real-world control tasks, such as robotics. However, the trial-and-error nature of these methods poses safety issues whenever the learning process itself must be performed on a physical system or involves any form of human-computer interaction. In this paper, we address a specific safety formulation, where both goals and dangers are encoded in a scalar reward signal and the learning agent is constrained to never worsen its performance, measured as the expected sum of rewards. By studying actor-only PG from a stochastic optimization perspective, we establish improvement guarantees for a wide class of parametric policies, generalizing existing results on Gaussian policies. This, together with novel upper bounds on the variance of PG estimators, allows us to identify meta-parameter schedules that guarantee monotonic improvement with high probability. The two key meta-parameters are the step size of the parameter updates and the batch size of the gradient estimates. Through a joint, adaptive selection of these meta-parameters, we obtain a PG algorithm with monotonic improvement guarantees.

Multi-Armed Bandit (MAB) techniques have been successfully applied to many classes of sequential decision problems in the past decades. However, non-stationary settings -- very common in real-world applications -- received little attention so far, and theoretical guarantees on the regret are known only for some frequentist algorithms. In this paper, we propose an algorithm, namely Sliding-Window Thompson Sampling (SW-TS), for nonstationary stochastic MAB settings. Our algorithm is based on Thompson Sampling and exploits a sliding-window approach to tackle, in a unified fashion, two different forms of non-stationarity studied separately so far: abruptly changing and smoothly changing. In the former, the reward distributions are constant during sequences of rounds, and their change may be arbitrary and happen at unknown rounds, while, in the latter, the reward distributions smoothly evolve over rounds according to unknown dynamics. Under mild assumptions, we provide regret upper bounds on the dynamic pseudo-regret of SW-TS for the abruptly changing environment, for the smoothly changing one, and for the setting in which both the non-stationarity forms are present. Furthermore, we empirically show that SW-TS dramatically outperforms state-of-the-art algorithms even when the forms of non-stationarity are taken separately, as previously studied in the literature.

We study the problem of identifying the policy space available to an agent in a learning process, having access to a set of demonstrations generated by the agent playing the optimal policy in the considered space. We introduce an approach based on frequentist statistical testing to identify the set of policy parameters that the agent can control, within a larger parametric policy space. After presenting two identification rules (combinatorial and simplified), applicable under different assumptions on the policy space, we provide a probabilistic analysis of the simplified one in the case of linear policies belonging to the exponential family. To improve the performance of our identification rules, we make use of the recently introduced framework of the Configurable Markov Decision Processes, exploiting the opportunity of configuring the environment to induce the agent to reveal which parameters it can control. Finally, we provide an empirical evaluation, on both discrete and continuous domains, to prove the effectiveness of our identification rules.

One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select a small number of the relevant, nonredundant features to preserve the complete information contained in the original dataset, with little collinearity among features. This procedure helps mitigate problems like overfitting and the curse of dimensionality, which arise when dealing with high-dimensional problems. On the other hand, it is not desirable to simply discard some features, since they may still contain information that can be exploited to improve results. Instead, dimensionality reduction techniques are designed to limit the number of features in a dataset by projecting them into a lower dimensional space, possibly considering all the original features. However, the projected features resulting from the application of dimensionality reduction techniques are usually difficult to interpret. In this paper, we seek to design a principled dimensionality reduction approach that maintains the interpretability of the resulting features. Specifically, we propose a bias-variance analysis for linear models and we leverage these theoretical results to design an algorithm, Linear Correlated Features Aggregation (LinCFA), which aggregates groups of continuous features with their average if their correlation is “sufficiently large”. In this way, all features are considered, the dimensionality is reduced and the interpretability is preserved. Finally, we provide numerical validations of the proposed algorithm both on synthetic datasets to confirm the theoretical results and on real datasets to show some promising applications.

Many real-world control applications, from economics to robotics, are characterized by the presence of multiple conflicting objectives. In these problems, the standard concept of optimality is replaced by Pareto-optimality and the goal is to find the Pareto frontier, a set of solutions representing different compromises among the objectives. Despite recent advances in multi-objective optimization, achieving an accurate representation of the Pareto frontier is still an important challenge. In this paper, we propose a reinforcement learning policy gradient approach to learn a continuous approximation of the Pareto frontier in multi-objective Markov Decision Problems (MOMDPs). Differently from previous policy gradient algorithms, where n optimization routines are executed to have n solutions, our approach performs a single gradient ascent run, generating at each step an improved continuous approximation of the Pareto frontier. The idea is to optimize the parameters of a function defining a manifold in the policy parameters space, so that the corresponding image in the objectives space gets as close as possible to the true Pareto frontier. Besides deriving how to compute and estimate such gradient, we will also discuss the non-trivial issue of defining a metric to assess the quality of the candidate Pareto frontiers. Finally, the properties of the proposed approach are empirically evaluated on two problems, a linear-quadratic Gaussian regulator and a water reservoir control task.

Several variance-reduced versions of REINFORCE based on importance sampling achieve an improved O ( ϵ - 3 ) sample complexity to find an ϵ -stationary point, under an unrealistic assumption on the variance of the importance weights. In this paper, we propose the Defensive Policy Gradient (DEF-PG) algorithm, based on defensive importance sampling, achieving the same result without any assumption on the variance of the importance weights. We also show that this is not improvable by establishing a matching Ω ( ϵ - 3 ) lower bound, and that REINFORCE with its O ( ϵ - 4 ) sample complexity is actually optimal under weaker assumptions on the policy class. Numerical simulations show promising results for the proposed technique compared to similar algorithms based on vanilla importance sampling.