Damien Ernst

Pascal Leroy, Pablo G. Morato, Jonathan Pisane et al.

We introduce IMP-MARL, an open-source suite of multi-agent reinforcement learning (MARL) environments for large-scale Infrastructure Management Planning (IMP), offering a platform for benchmarking the scalability of cooperative MARL methods in real-world engineering applications. In IMP, a multi-component engineering system is subject to a risk of failure due to its components' damage condition. Specifically, each agent plans inspections and repairs for a specific system component, aiming to minimise maintenance costs while cooperating to minimise system failure risk. With IMP-MARL, we release several environments including one related to offshore wind structural systems, in an effort to meet today's needs to improve management strategies to support sustainable and reliable energy systems. Supported by IMP practical engineering environments featuring up to 100 agents, we conduct a benchmark campaign, where the scalability and performance of state-of-the-art cooperative MARL methods are compared against expert-based heuristic policies. The results reveal that centralised training with decentralised execution methods scale better with the number of agents than fully centralised or decentralised RL approaches, while also outperforming expert-based heuristic policies in most IMP environments. Based on our findings, we additionally outline remaining cooperation and scalability challenges that future MARL methods should still address. Through IMP-MARL, we encourage the implementation of new environments and the further development of MARL methods.

Spyros Chatzivasileiadis, Damien Ernst, Göran Andersson

This paper puts forward the vision that a natural future stage of the electricity network could be a grid spanning the whole planet and connecting most of the large power plants in the world: this is the "Global Grid". The main driving force behind the Global Grid will be the harvesting of remote renewable sources, and its key infrastructure element will be the high capacity long transmission lines. Wind farms and solar power plants will supply load centers with green power over long distances. This paper focuses on the introduction of the concept, showing that a globally interconnected network can be technologically feasible and economically competitive. We further highlight the multiple opportunities emerging from a global electricity network such as smoothing the renewable energy supply and electricity demand, reducing the need for bulk storage, and reducing the volatility of the energy prices. We also discuss possible investment mechanisms and operating schemes. Among others, we envision in such a system a global power market and the establishment of two new coordinating bodies, the "Global Regulator" and the "Global System Operator".

Aivar Sootla, Alexandre Mauroy, Damien Ernst

In many applications, and in systems/synthetic biology, in particular, it is desirable to compute control policies that force the trajectory of a bistable system from one equilibrium (the initial point) to another equilibrium (the target point), or in other words to solve the switching problem. It was recently shown that, for monotone bistable systems, this problem admits easy-to-implement open-loop solutions in terms of temporal pulses (i.e., step functions of fixed length and fixed magnitude). In this paper, we develop this idea further and formulate a problem of convergence to an equilibrium from an arbitrary initial point. We show that this problem can be solved using a static optimization problem in the case of monotone systems. Changing the initial point to an arbitrary state allows to build closed-loop, event-based or open-loop policies for the switching/convergence problems. In our derivations we exploit the Koopman operator, which offers a linear infinite-dimensional representation of an autonomous nonlinear system. One of the main advantages of using the Koopman operator is the powerful computational tools developed for this framework. Besides the presence of numerical solutions, the switching/convergence problem can also serve as a building block for solving more complicated control problems and can potentially be applied to non-monotone systems. We illustrate this argument on the problem of synchronizing cardiac cells by defibrillation. Potentially, our approach can be extended to problems with different parametrizations of control signals since the only fundamental limitation is the finite time application of the control signal.

Quentin Gemine, Damien Ernst, Bertrand Cornélusse

With the increasing share of renewable and distributed generation in electrical distribution systems, Active Network Management (ANM) becomes a valuable option for a distribution system operator to operate his system in a secure and cost-effective way without relying solely on network reinforcement. ANM strategies are short-term policies that control the power injected by generators and/or taken off by loads in order to avoid congestion or voltage issues. Advanced ANM strategies imply that the system operator has to solve large-scale optimal sequential decision-making problems under uncertainty. For example, decisions taken at a given moment constrain the future decisions that can be taken and uncertainty must be explicitly accounted for because neither demand nor generation can be accurately forecasted. We first formulate the ANM problem, which in addition to be sequential and uncertain, has a nonlinear nature stemming from the power flow equations and a discrete nature arising from the activation of power modulation signals. This ANM problem is then cast as a stochastic mixed-integer nonlinear program, as well as second-order cone and linear counterparts, for which we provide quantitative results using state of the art solvers and perform a sensitivity analysis over the size of the system, the amount of available flexibility, and the number of scenarios considered in the deterministic equivalent of the stochastic program. To foster further research on this problem, we make available at http://www.montefiore.ulg.ac.be/~anm/ three test beds based on distribution networks of 5, 33, and 77 buses. These test beds contain a simulator of the distribution system, with stochastic models for the generation and consumption devices, and callbacks to implement and test various ANM strategies.

Gaspard Lambrechts, Adrien Bolland, Damien Ernst

Reinforcement learning aims to learn optimal policies from interaction with environments whose dynamics are unknown. Many methods rely on the approximation of a value function to derive near-optimal policies. In partially observable environments, these functions depend on the complete sequence of observations and past actions, called the history. In this work, we show empirically that recurrent neural networks trained to approximate such value functions internally filter the posterior probability distribution of the current state given the history, called the belief. More precisely, we show that, as a recurrent neural network learns the Q-function, its hidden states become more and more correlated with the beliefs of state variables that are relevant to optimal control. This correlation is measured through their mutual information. In addition, we show that the expected return of an agent increases with the ability of its recurrent architecture to reach a high mutual information between its hidden states and the beliefs. Finally, we show that the mutual information between the hidden states and the beliefs of variables that are irrelevant for optimal control decreases through the learning process. In summary, this work shows that in its hidden states, a recurrent neural network approximating the Q-function of a partially observable environment reproduces a sufficient statistic from the history that is correlated to the relevant part of the belief for taking optimal actions.

Aivar Sootla, Natalja Strelkowa, Damien Ernst et al.

In this paper, we consider the periodic reference tracking problem in the framework of batch-mode reinforcement learning, which studies methods for solving optimal control problems from the sole knowledge of a set of trajectories. In particular, we extend an existing batch-mode reinforcement learning algorithm, known as Fitted Q Iteration, to the periodic reference tracking problem. The presented periodic reference tracking algorithm explicitly exploits a priori knowledge of the future values of the reference trajectory and its periodicity. We discuss the properties of our approach and illustrate it on the problem of reference tracking for a synthetic biology gene regulatory network known as the generalised repressilator. This system can produce decaying but long-lived oscillations, which makes it an interesting system for the tracking problem. In our companion paper we also take a look at the regulation problem of the toggle switch system, where the main goal is to drive the system's states to a specific bounded region in the state space.

Gaspard Lambrechts, Adrien Bolland, Damien Ernst

In this work, we generalize the problem of learning through interaction in a POMDP by accounting for eventual additional information available at training time. First, we introduce the informed POMDP, a new learning paradigm offering a clear distinction between the information at training and the observation at execution. Next, we propose an objective that leverages this information for learning a sufficient statistic of the history for the optimal control. We then adapt this informed objective to learn a world model able to sample latent trajectories. Finally, we empirically show a learning speed improvement in several environments using this informed world model in the Dreamer algorithm. These results and the simplicity of the proposed adaptation advocate for a systematic consideration of eventual additional information when learning in a POMDP using model-based RL.

Thibaut Théate, Damien Ernst

Classical reinforcement learning (RL) techniques are generally concerned with the design of decision-making policies driven by the maximisation of the expected outcome. Nevertheless, this approach does not take into consideration the potential risk associated with the actions taken, which may be critical in certain applications. To address that issue, the present research work introduces a novel methodology based on distributional RL to derive sequential decision-making policies that are sensitive to the risk, the latter being modelled by the tail of the return probability distribution. The core idea is to replace the $Q$ function generally standing at the core of learning schemes in RL by another function taking into account both the expected return and the risk. Named the risk-based utility function $U$, it can be extracted from the random return distribution $Z$ naturally learnt by any distributional RL algorithm. This enables to span the complete potential trade-off between risk minimisation and expected return maximisation, in contrast to fully risk-averse methodologies. Fundamentally, this research yields a truly practical and accessible solution for learning risk-sensitive policies with minimal modification to the distributional RL algorithm, and with an emphasis on the interpretability of the resulting decision-making process.

Pascal Leroy, Jonathan Pisane, Damien Ernst

In this paper, we identify the best learning scenario to train a team of agents to compete against multiple possible strategies of opposing teams. We evaluate cooperative value-based methods in a mixed cooperative-competitive environment. We restrict ourselves to the case of a symmetric, partially observable, two-team Markov game. We selected three training methods based on the centralised training and decentralised execution (CTDE) paradigm: QMIX, MAVEN and QVMix. For each method, we considered three learning scenarios differentiated by the variety of team policies encountered during training. For our experiments, we modified the StarCraft Multi-Agent Challenge environment to create competitive environments where both teams could learn and compete simultaneously. Our results suggest that training against multiple evolving strategies achieves the best results when, for scoring their performances, teams are faced with several strategies.

Florent De Geeter, Damien Ernst, Guillaume Drion

Spiking neural networks are a type of artificial neural networks in which communication between neurons is only made of events, also called spikes. This property allows neural networks to make asynchronous and sparse computations and therefore drastically decrease energy consumption when run on specialised hardware. However, training such networks is known to be difficult, mainly due to the non-differentiability of the spike activation, which prevents the use of classical backpropagation. This is because state-of-the-art spiking neural networks are usually derived from biologically-inspired neuron models, to which are applied machine learning methods for training. Nowadays, research about spiking neural networks focuses on the design of training algorithms whose goal is to obtain networks that compete with their non-spiking version on specific tasks. In this paper, we attempt the symmetrical approach: we modify the dynamics of a well-known, easily trainable type of recurrent neural network to make it event-based. This new RNN cell, called the Spiking Recurrent Cell, therefore communicates using events, i.e. spikes, while being completely differentiable. Vanilla backpropagation can thus be used to train any network made of such RNN cell. We show that this new network can achieve performance comparable to other types of spiking networks in the MNIST benchmark and its variants, the Fashion-MNIST and the Neuromorphic-MNIST. Moreover, we show that this new cell makes the training of deep spiking networks achievable.

Florent De Geeter, Gaspard Lambrechts, Damien Ernst et al.

With the emergence of massively parallel processing units, parallelization has become a desirable property for new sequence models. The ability to parallelize the processing of sequences with respect to the sequence length during training is one of the main factors behind the uprising of the Transformer architecture. However, Transformers lack efficiency at sequence generation, as they need to reprocess all past timesteps at every generation step. Recently, state-space models (SSMs) emerged as a more efficient alternative. These new kinds of recurrent neural networks (RNNs) keep the efficient update of the RNNs while gaining parallelization by getting rid of nonlinear dynamics (or recurrence). SSMs can reach state-of-the art performance through the efficient training of potentially very large networks, but still suffer from limited representation capabilities. In particular, SSMs cannot exhibit persistent memory, or the capacity of retaining information for an infinite duration, because of their monostability. In this paper, we introduce a new family of RNNs, the memory recurrent units (MRUs), that combine the persistent memory capabilities of nonlinear RNNs with the parallelizable computations of SSMs. These units leverage multistability as a source of persistent memory, while getting rid of transient dynamics for efficient computations. We then derive a specific implementation as proof-of-concept: the bistable memory recurrent unit (BMRU). This new RNN is compatible with the parallel scan algorithm. We show that BMRU achieves good results in tasks with long-term dependencies, and can be combined with state-space models to create hybrid networks that are parallelizable and have transient dynamics as well as persistent memory.

Maurizio Vassallo, Amina Benzerga, Alireza Bahmanyar et al.

The increasing adoption of distributed energy resources, particularly photovoltaic (PV) panels, has presented new and complex challenges for power network control. With the significant energy production from PV panels, voltage issues in the network have become a problem. Currently, PV smart inverters (SIs) are used to mitigate the voltage problems by controlling their active power generation and reactive power injection or absorption. However, reducing the active power output of PV panels can be perceived as unfair to some customers, discouraging future installations. To solve this issue, in this paper, a reinforcement learning technique is proposed to address voltage issues in a distribution network, while considering fairness in active power curtailment among customers. The feasibility of the proposed approach is explored through experiments, demonstrating its ability to effectively control voltage in a fair and efficient manner.

Gaspard Lambrechts, Yann Claes, Pierre Geurts et al.

Attention-based models such as Transformers and recurrent models like state space models (SSMs) have emerged as successful methods for autoregressive sequence modeling. Although both enable parallel training, none enable parallel generation due to their autoregressiveness. We propose the variational SSM (VSSM), a variational autoencoder (VAE) where both the encoder and decoder are SSMs. Since sampling the latent variables and decoding them with the SSM can be parallelized, both training and generation can be conducted in parallel. Moreover, the decoder recurrence allows generation to be resumed without reprocessing the whole sequence. Finally, we propose the autoregressive VSSM that can be conditioned on a partial realization of the sequence, as is common in language generation tasks. Interestingly, the autoregressive VSSM still enables parallel generation. We highlight on toy problems (MNIST, CIFAR) the empirical gains in speed-up and show that it competes with traditional models in terms of generation quality (Transformer, Mamba SSM).

Julien Brandoit, Damien Ernst, Guillaume Drion et al.

Neurons communicate through spikes, and spike timing is a crucial part of neuronal processing. Spike times can be recorded experimentally both intracellularly and extracellularly, and are the main output of state-of-the-art neural probes. On the other hand, neuronal activity is controlled at the molecular level by the currents generated by many different transmembrane proteins called ion channels. Connecting spike timing to ion channel composition remains an arduous task to date. To address this challenge, we developed a method that combines deep learning with a theoretical tool called Dynamic Input Conductances (DICs), which reduce the complexity of ion channel interactions into three interpretable components describing how neurons spike. Our approach uses deep learning to infer DICs directly from spike times and then generates populations of "twin" neuron models that replicate the observed activity while capturing natural variability in membrane channel composition. The method is fast, accurate, and works using only spike recordings. We also provide open-source software with a graphical interface, making it accessible to researchers without programming expertise.

Julien Brandoit, Arthur Fyon, Damien Ernst et al.

Sequence learning is dominated by Transformers and parallelizable recurrent neural networks (RNNs) such as state-space models, yet learning long-term dependencies remains challenging, and state-of-the-art designs trade power consumption for performance. The Bistable Memory Recurrent Unit (BMRU) was introduced to enable hardware-software co-design of ultra-low power RNNs: quantized states with hysteresis provide persistent memory while mapping directly to analog primitives. However, BMRU performance lags behind parallelizable RNNs on complex sequential tasks. In this paper, we identify gradient blocking during state updates as a key limitation and propose a cumulative update formulation that restores gradient flow while preserving persistent memory, creating skip-connections through time. This leads to the Cumulative Memory Recurrent Unit (CMRU) and its relaxed variant, the $α$CMRU. Experiments show that the cumulative formulation dramatically improves convergence stability and reduces initialization sensitivity. The CMRU and $α$CMRU match or outperform Linear Recurrent Units (LRUs) and minimal Gated Recurrent Units (minGRUs) across diverse benchmarks at small model sizes, with particular advantages on tasks requiring discrete long-range retention, while the CMRU retains quantized states, persistent memory, and noise-resilient dynamics essential for analog implementation.

Arthur Fyon, Julien Brandoit, Loris Mendolia et al.

Always-on AI applications, from environmental sensors to biomedical implants, require ultra-low power consumption. Analog circuits offer a path to sub-microwatt inference, yet existing analog implementations are limited to feedforward architectures: extending them to recurrent dynamics has been considered impractical due to noise accumulation through temporal feedback. We demonstrate that this barrier can be overcome through hardware-software co-design. Specifically, we identify that Bistable Memory Recurrent Units (BMRUs), a class of Recurrent Neural Networks (RNNs) with discrete-valued outputs and hysteretic dynamics, admit an ultra-low power current-mode analog implementation which we design from first principles. The resulting circuit establishes a one-to-one correspondence between each learned parameter and a circuit element. The discrete outputs suppress analog noise by at least 20-fold at each cell boundary, breaking the noise accumulation that prevents analog recurrence. We reformulate BMRUs for first-quadrant operation with fixed thresholds, enabling the direct correspondence while preserving expressivity and trainability. Transistor-level simulations in 180 nm Complementary Metal-Oxide-Semiconductor (CMOS) show near-perfect agreement between software predictions and circuit-level behavior, with the software model thereby serving as a high-fidelity simulator of the physical hardware at low computational cost. We leverage this fidelity to conduct large-scale noise immunity and power scaling analyses: the power cost of adding recurrence scales linearly with state dimension, while the feedforward layers dominating total power scale quadratically, meaning recurrence is added at linear marginal cost relative to the feedforward backbone. End-to-end keyword spotting achieves sub-microwatt inference at the RNN core.

Adrien Bolland, Gaspard Lambrechts, Damien Ernst

Maximum entropy reinforcement learning motivates agents to explore states and actions to maximize the entropy of some distribution, typically by providing additional intrinsic rewards proportional to that entropy function. In this paper, we study intrinsic rewards proportional to the entropy of the discounted distribution of state-action features visited during future time steps. This approach is motivated by two results. First, we show that the expected sum of these intrinsic rewards is a lower bound on the entropy of the discounted distribution of state-action features visited in trajectories starting from the initial states, which we relate to an alternative maximum entropy objective. Second, we show that the distribution used in the intrinsic reward definition is the fixed point of a contraction operator and can therefore be estimated off-policy. Experiments highlight that the new objective leads to improved visitation of features within individual trajectories, in exchange for slightly reduced visitation of features in expectation over different trajectories, as suggested by the lower bound. It also leads to improved convergence speed for learning exploration-only agents. Control performance remains similar across most methods on the considered benchmarks.

Michaël Fonder, Damien Ernst, Marc Van Droogenbroeck

Estimating the distance to objects is crucial for autonomous vehicles when using depth sensors is not possible. In this case, the distance has to be estimated from on-board mounted RGB cameras, which is a complex task especially in environments such as natural outdoor landscapes. In this paper, we present a new method named M4Depth for depth estimation. First, we establish a bijective relationship between depth and the visual disparity of two consecutive frames and show how to exploit it to perform motion-invariant pixel-wise depth estimation. Then, we detail M4Depth which is based on a pyramidal convolutional neural network architecture where each level refines an input disparity map estimate by using two customized cost volumes. We use these cost volumes to leverage the visual spatio-temporal constraints imposed by motion and to make the network robust for varied scenes. We benchmarked our approach both in test and generalization modes on public datasets featuring synthetic camera trajectories recorded in a wide variety of outdoor scenes. Results show that our network outperforms the state of the art on these datasets, while also performing well on a standard depth estimation benchmark. The code of our method is publicly available at https://github.com/michael-fonder/M4Depth.

Robin Henry, Damien Ernst

Active network management (ANM) of electricity distribution networks include many complex stochastic sequential optimization problems. These problems need to be solved for integrating renewable energies and distributed storage into future electrical grids. In this work, we introduce Gym-ANM, a framework for designing reinforcement learning (RL) environments that model ANM tasks in electricity distribution networks. These environments provide new playgrounds for RL research in the management of electricity networks that do not require an extensive knowledge of the underlying dynamics of such systems. Along with this work, we are releasing an implementation of an introductory toy-environment, ANM6-Easy, designed to emphasize common challenges in ANM. We also show that state-of-the-art RL algorithms can already achieve good performance on ANM6-Easy when compared against a model predictive control (MPC) approach. Finally, we provide guidelines to create new Gym-ANM environments differing in terms of (a) the distribution network topology and parameters, (b) the observation space, (c) the modelling of the stochastic processes present in the system, and (d) a set of hyperparameters influencing the reward signal. Gym-ANM can be downloaded at https://github.com/robinhenry/gym-anm.

Michael Castronovo, Damien Ernst, Adrien Couetoux et al.

In the Bayesian Reinforcement Learning (BRL) setting, agents try to maximise the collected rewards while interacting with their environment while using some prior knowledge that is accessed beforehand. Many BRL algorithms have already been proposed, but even though a few toy examples exist in the literature, there are still no extensive or rigorous benchmarks to compare them. The paper addresses this problem, and provides a new BRL comparison methodology along with the corresponding open source library. In this methodology, a comparison criterion that measures the performance of algorithms on large sets of Markov Decision Processes (MDPs) drawn from some probability distributions is defined. In order to enable the comparison of non-anytime algorithms, our methodology also includes a detailed analysis of the computation time requirement of each algorithm. Our library is released with all source code and documentation: it includes three test problems, each of which has two different prior distributions, and seven state-of-the-art RL algorithms. Finally, our library is illustrated by comparing all the available algorithms and the results are discussed.

Matthias Pirlet, Adrien Bolland, Gilles Louppe et al.

The Unit Commitment (UC) problem is a key optimization task in power systems to forecast the generation schedules of power units over a finite time period by minimizing costs while meeting demand and technical constraints. However, many parameters required by the UC problem are unknown, such as the costs. In this work, we estimate these unknown costs using simulation-based inference on an illustrative UC problem, which provides an approximated posterior distribution of the parameters given observed generation schedules and demands. Our results highlight that the learned posterior distribution effectively captures the underlying distribution of the data, providing a range of possible values for the unknown parameters given a past observation. This posterior allows for the estimation of past costs using observed past generation schedules, enabling operators to better forecast future costs and make more robust generation scheduling forecasts. We present avenues for future research to address overconfidence in posterior estimation, enhance the scalability of the methodology and apply it to more complex UC problems modeling the network constraints and renewable energy sources.

Adrien Bolland, Gaspard Lambrechts, Damien Ernst

Maximum entropy reinforcement learning integrates exploration into policy learning by providing additional intrinsic rewards proportional to the entropy of some distribution. In this paper, we propose a novel approach in which the intrinsic reward function is the relative entropy of the discounted distribution of states and actions (or features derived from these states and actions) visited during future time steps. This approach is motivated by two results. First, a policy maximizing the expected discounted sum of intrinsic rewards also maximizes a lower bound on the state-action value function of the decision process. Second, the distribution used in the intrinsic reward definition is the fixed point of a contraction operator. Existing algorithms can therefore be adapted to learn this fixed point off-policy and to compute the intrinsic rewards. We finally introduce an algorithm maximizing our new objective, and we show that resulting policies have good state-action space coverage and achieve high-performance control.

Matthias Pirlet, Adrien Bolland, Alexandre Huynen et al.

Estimating generation costs from observed electricity market data is essential for market simulation, strategic bidding, and system planning. To that end, we model the relationship between generation costs and production schedules with a latent variable model. Estimating generation costs from observed schedules is then formulated as Bayesian inference. A prior distribution encodes an initial belief on parameters, and the inference consists of updating the belief with the posterior distribution given observations. We use balanced neural posterior estimation (BNPE) to learn this posterior. Validation on the IEEE RTS-96 test system shows that marginal costs are recovered with narrow credible intervals, while start-up costs remain largely unidentifiable from schedules alone. The method is benchmarked against an inverse-optimization algorithm that exhibits larger parameter errors without uncertainty quantification.

Gaspard Lambrechts, Damien Ernst, Aditya Mahajan

In reinforcement learning for partially observable environments, many successful algorithms have been developed within the asymmetric learning paradigm. This paradigm leverages additional state information available at training time for faster learning. Although the proposed learning objectives are usually theoretically sound, these methods still lack a precise theoretical justification for their potential benefits. We propose such a justification for asymmetric actor-critic algorithms with linear function approximators by adapting a finite-time convergence analysis to this setting. The resulting finite-time bound reveals that the asymmetric critic eliminates error terms arising from aliasing in the agent state.

Adrien Bolland, Gaspard Lambrechts, Damien Ernst

In order to compute near-optimal policies with policy-gradient algorithms, it is common in practice to include intrinsic exploration terms in the learning objective. Although the effectiveness of these terms is usually justified by an intrinsic need to explore environments, we propose a novel analysis with the lens of numerical optimization. Two criteria are introduced on the learning objective and two others on its stochastic gradient estimates, and are afterwards used to discuss the quality of the policy after optimization. The analysis sheds light on two separate effects of exploration techniques. First, they make it possible to smooth the learning objective and to eliminate local optima while preserving the global maximum. Second, they modify the gradient estimates, increasing the probability that the stochastic parameter updates eventually provide an optimal policy. We empirically illustrate these effects with exploration strategies based on entropy bonuses, identifying limitations and suggesting directions for future work.

Antoine Mouchamps, Arthur Malherbe, Adrien Bolland et al.

This paper presents Gym-TORAX, a Python package enabling the implementation of Reinforcement Learning (RL) environments for simulating plasma dynamics and control in tokamaks. Users define succinctly a set of control actions and observations, and a control objective from which Gym-TORAX creates a Gymnasium environment that wraps TORAX for simulating the plasma dynamics. The objective is formulated through rewards depending on the simulated state of the plasma and control action to optimize specific characteristics of the plasma, such as performance and stability. The resulting environment instance is then compatible with a wide range of RL algorithms and libraries and will facilitate RL research in plasma control. In its current version, one environment is readily available, based on a ramp-up scenario of the International Thermonuclear Experimental Reactor (ITER).

Daniel Ebi, Gaspard Lambrechts, Damien Ernst et al.

Reinforcement learning in partially observable environments requires agents to act under uncertainty from noisy, incomplete observations. Asymmetric actor-critic methods leverage privileged information during training to improve learning under these conditions. However, existing approaches typically assume full-state access during training. In this work, we challenge this assumption by proposing a novel actor-critic framework, called informed asymmetric actor-critic, that enables conditioning the critic on arbitrary privileged signals without requiring access to the full state. We show that policy gradients remain unbiased under this formulation, extending the theoretical foundation of asymmetric methods to the more general case of privileged partial information. To quantify the impact of such signals, we propose informativeness measures based on kernel methods and return prediction error, providing practical tools for evaluating training-time signals. We validate our approach empirically on benchmark navigation tasks and synthetic partially observable environments, showing that our informed asymmetric method improves learning efficiency and value estimation when informative privileged inputs are available. Our findings challenge the necessity of full-state access and open new directions for designing asymmetric reinforcement learning methods that are both practical and theoretically sound.

Laurie Boveroux, Damien Ernst, Quentin Louveaux

The Job Shop Scheduling Problem (JSSP) is a well-known optimization problem in manufacturing, where the goal is to determine the optimal sequence of jobs across different machines to minimize a given objective. In this work, we focus on minimising the weighted sum of job completion times. We explore the potential of Monte Carlo Tree Search (MCTS), a heuristic-based reinforcement learning technique, to solve large-scale JSSPs, especially those with recirculation. We propose several Markov Decision Process (MDP) formulations to model the JSSP for the MCTS algorithm. In addition, we introduce a new synthetic benchmark derived from real manufacturing data, which captures the complexity of large, non-rectangular instances often encountered in practice. Our experimental results show that MCTS effectively produces good-quality solutions for large-scale JSSP instances, outperforming our constraint programming approach.

Adrien Bolland, Gilles Louppe, Damien Ernst

Direct policy optimization in reinforcement learning is usually solved with policy-gradient algorithms, which optimize policy parameters via stochastic gradient ascent. This paper provides a new theoretical interpretation and justification of these algorithms. First, we formulate direct policy optimization in the optimization by continuation framework. The latter is a framework for optimizing nonconvex functions where a sequence of surrogate objective functions, called continuations, are locally optimized. Second, we show that optimizing affine Gaussian policies and performing entropy regularization can be interpreted as implicitly optimizing deterministic policies by continuation. Based on these theoretical results, we argue that exploration in policy-gradient algorithms consists in computing a continuation of the return of the policy at hand, and that the variance of policies should be history-dependent functions adapted to avoid local extrema rather than to maximize the return of the policy.

Florian Merchie, Damien Ernst

In business retention, churn prevention has always been a major concern. This work contributes to this domain by formalizing the problem of churn prediction in the context of online gambling as a binary classification task. We also propose an algorithmic answer to this problem based on recurrent neural network. This algorithm is tested with online gambling data that have the form of time series, which can be efficiently processed by recurrent neural networks. To evaluate the performances of the trained models, standard machine learning metrics were used, such as accuracy, precision and recall. For this problem in particular, the conducted experiments allowed to assess that the choice of a specific architecture depends on the metric which is given the greatest importance. Architectures using nBRC favour precision, those using LSTM give better recall, while GRU-based architectures allow a higher accuracy and balance two other metrics. Moreover, further experiments showed that using only the more recent time-series histories to train the networks decreases the quality of the results. We also study the performances of models learned at a specific instant $t$, at other times $t^{\prime} > t$. The results show that the performances of the models learned at time $t$ remain good at the following instants $t^{\prime} > t$, suggesting that there is no need to refresh the models at a high rate. However, the performances of the models were subject to noticeable variance due to one-off events impacting the data.

Thibaut Théate, Antoine Wehenkel, Adrien Bolland et al.

The distributional reinforcement learning (RL) approach advocates for representing the complete probability distribution of the random return instead of only modelling its expectation. A distributional RL algorithm may be characterised by two main components, namely the representation of the distribution together with its parameterisation and the probability metric defining the loss. The present research work considers the unconstrained monotonic neural network (UMNN) architecture, a universal approximator of continuous monotonic functions which is particularly well suited for modelling different representations of a distribution. This property enables the efficient decoupling of the effect of the function approximator class from that of the probability metric. The research paper firstly introduces a methodology for learning different representations of the random return distribution (PDF, CDF and QF). Secondly, a novel distributional RL algorithm named unconstrained monotonic deep Q-network (UMDQN) is presented. To the authors' knowledge, it is the first distributional RL method supporting the learning of three, valid and continuous representations of the random return distribution. Lastly, in light of this new algorithm, an empirical comparison is performed between three probability quasi-metrics, namely the Kullback-Leibler divergence, Cramer distance, and Wasserstein distance. The results highlight the main strengths and weaknesses associated with each probability metric together with an important limitation of the Wasserstein distance.

Gaspard Lambrechts, Florent De Geeter, Nicolas Vecoven et al.

Training recurrent neural networks is known to be difficult when time dependencies become long. In this work, we show that most standard cells only have one stable equilibrium at initialisation, and that learning on tasks with long time dependencies generally occurs once the number of network stable equilibria increases; a property known as multistability. Multistability is often not easily attained by initially monostable networks, making learning of long time dependencies between inputs and outputs difficult. This insight leads to the design of a novel way to initialise any recurrent cell connectivity through a procedure called "warmup" to improve its capability to learn arbitrarily long time dependencies. This initialisation procedure is designed to maximise network reachable multistability, i.e., the number of equilibria within the network that can be reached through relevant input trajectories, in few gradient steps. We show on several information restitution, sequence classification, and reinforcement learning benchmarks that warming up greatly improves learning speed and performance, for multiple recurrent cells, but sometimes impedes precision. We therefore introduce a double-layer architecture initialised with a partial warmup that is shown to greatly improve learning of long time dependencies while maintaining high levels of precision. This approach provides a general framework for improving learning abilities of any recurrent cell when long time dependencies are present. We also show empirically that other initialisation and pretraining procedures from the literature implicitly foster reachable multistability of recurrent cells.

Robin Henry, Damien Ernst

Gym-ANM is a Python package that facilitates the design of reinforcement learning (RL) environments that model active network management (ANM) tasks in electricity networks. Here, we describe how to implement new environments and how to write code to interact with pre-existing ones. We also provide an overview of ANM6-Easy, an environment designed to highlight common ANM challenges. Finally, we discuss the potential impact of Gym-ANM on the scientific community, both in terms of research and education. We hope this package will facilitate collaboration between the power system and RL communities in the search for algorithms to control future energy systems.

Decebal Constantin Mocanu, Elena Mocanu, Tiago Pinto et al.

A fundamental task for artificial intelligence is learning. Deep Neural Networks have proven to cope perfectly with all learning paradigms, i.e. supervised, unsupervised, and reinforcement learning. Nevertheless, traditional deep learning approaches make use of cloud computing facilities and do not scale well to autonomous agents with low computational resources. Even in the cloud, they suffer from computational and memory limitations, and they cannot be used to model adequately large physical worlds for agents which assume networks with billions of neurons. These issues are addressed in the last few years by the emerging topic of sparse training, which trains sparse networks from scratch. This paper discusses sparse training state-of-the-art, its challenges and limitations while introducing a couple of new theoretical research directions which has the potential of alleviating sparse training limitations to push deep learning scalability well beyond its current boundaries. Nevertheless, the theoretical advancements impact in complex multi-agents settings is discussed from a real-world perspective, using the smart grid case study.

Pascal Leroy, Damien Ernst, Pierre Geurts et al.

This paper introduces four new algorithms that can be used for tackling multi-agent reinforcement learning (MARL) problems occurring in cooperative settings. All algorithms are based on the Deep Quality-Value (DQV) family of algorithms, a set of techniques that have proven to be successful when dealing with single-agent reinforcement learning problems (SARL). The key idea of DQV algorithms is to jointly learn an approximation of the state-value function $V$, alongside an approximation of the state-action value function $Q$. We follow this principle and generalise these algorithms by introducing two fully decentralised MARL algorithms (IQV and IQV-Max) and two algorithms that are based on the centralised training with decentralised execution training paradigm (QVMix and QVMix-Max). We compare our algorithms with state-of-the-art MARL techniques on the popular StarCraft Multi-Agent Challenge (SMAC) environment. We show competitive results when QVMix and QVMix-Max are compared to well-known MARL techniques such as QMIX and MAVEN and show that QVMix can even outperform them on some of the tested environments, being the algorithm which performs best overall. We hypothesise that this is due to the fact that QVMix suffers less from the overestimation bias of the $Q$ function.

Thibaut Théate, Sébastien Mathieu, Damien Ernst

Retailers and major consumers of electricity generally purchase an important percentage of their estimated electricity needs years ahead in the forward market. This long-term electricity procurement task consists of determining when to buy electricity so that the resulting energy cost is minimised, and the forecast consumption is covered. In this scientific article, the focus is set on a yearly base load product from the Belgian forward market, named calendar (CAL), which is tradable up to three years ahead of the delivery period. This research paper introduces a novel algorithm providing recommendations to either buy electricity now or wait for a future opportunity based on the history of CAL prices. This algorithm relies on deep learning forecasting techniques and on an indicator quantifying the deviation from a perfectly uniform reference procurement policy. On average, the proposed approach surpasses the benchmark procurement policies considered and achieves a reduction in costs of 1.65% with respect to the perfectly uniform reference procurement policy achieving the mean electricity price. Moreover, in addition to automating the complex electricity procurement task, this algorithm demonstrates more consistent results throughout the years. Eventually, the generality of the solution presented makes it well suited for solving other commodity procurement problems.

Nicolas Vecoven, Damien Ernst, Guillaume Drion

Recurrent neural networks (RNNs) provide state-of-the-art performances in a wide variety of tasks that require memory. These performances can often be achieved thanks to gated recurrent cells such as gated recurrent units (GRU) and long short-term memory (LSTM). Standard gated cells share a layer internal state to store information at the network level, and long term memory is shaped by network-wide recurrent connection weights. Biological neurons on the other hand are capable of holding information at the cellular level for an arbitrary long amount of time through a process called bistability. Through bistability, cells can stabilize to different stable states depending on their own past state and inputs, which permits the durable storing of past information in neuron state. In this work, we take inspiration from biological neuron bistability to embed RNNs with long-lasting memory at the cellular level. This leads to the introduction of a new bistable biologically-inspired recurrent cell that is shown to strongly improves RNN performance on time-series which require very long memory, despite using only cellular connections (all recurrent connections are from neurons to themselves, i.e. a neuron state is not influenced by the state of other neurons). Furthermore, equipping this cell with recurrent neuromodulation permits to link them to standard GRU cells, taking a step towards the biological plausibility of GRU.

Adrien Bolland, Ioannis Boukas, Mathias Berger et al.

We consider the joint design and control of discrete-time stochastic dynamical systems over a finite time horizon. We formulate the problem as a multi-step optimization problem under uncertainty seeking to identify a system design and a control policy that jointly maximize the expected sum of rewards collected over the time horizon considered. The transition function, the reward function and the policy are all parametrized, assumed known and differentiable with respect to their parameters. We then introduce a deep reinforcement learning algorithm combining policy gradient methods with model-based optimization techniques to solve this problem. In essence, our algorithm iteratively approximates the gradient of the expected return via Monte-Carlo sampling and automatic differentiation and takes projected gradient ascent steps in the space of environment and policy parameters. This algorithm is referred to as Direct Environment and Policy Search (DEPS). We assess the performance of our algorithm in three environments concerned with the design and control of a mass-spring-damper system, a small-scale off-grid power system and a drone, respectively. In addition, our algorithm is benchmarked against a state-of-the-art deep reinforcement learning algorithm used to tackle joint design and control problems. We show that DEPS performs at least as well or better in all three environments, consistently yielding solutions with higher returns in fewer iterations. Finally, solutions produced by our algorithm are also compared with solutions produced by an algorithm that does not jointly optimize environment and policy parameters, highlighting the fact that higher returns can be achieved when joint optimization is performed.

Ioannis Boukas, Damien Ernst, Thibaut Théate et al.

The large integration of variable energy resources is expected to shift a large part of the energy exchanges closer to real-time, where more accurate forecasts are available. In this context, the short-term electricity markets and in particular the intraday market are considered a suitable trading floor for these exchanges to occur. A key component for the successful renewable energy sources integration is the usage of energy storage. In this paper, we propose a novel modelling framework for the strategic participation of energy storage in the European continuous intraday market where exchanges occur through a centralized order book. The goal of the storage device operator is the maximization of the profits received over the entire trading horizon, while taking into account the operational constraints of the unit. The sequential decision-making problem of trading in the intraday market is modelled as a Markov Decision Process. An asynchronous distributed version of the fitted Q iteration algorithm is chosen for solving this problem due to its sample efficiency. The large and variable number of the existing orders in the order book motivates the use of high-level actions and an alternative state representation. Historical data are used for the generation of a large number of artificial trajectories in order to address exploration issues during the learning process. The resulting policy is back-tested and compared against a benchmark strategy that is the current industrial standard. Results indicate that the agent converges to a policy that achieves in average higher total revenues than the benchmark strategy.

Thibaut Théate, Damien Ernst

This scientific research paper presents an innovative approach based on deep reinforcement learning (DRL) to solve the algorithmic trading problem of determining the optimal trading position at any point in time during a trading activity in stock markets. It proposes a novel DRL trading strategy so as to maximise the resulting Sharpe ratio performance indicator on a broad range of stock markets. Denominated the Trading Deep Q-Network algorithm (TDQN), this new trading strategy is inspired from the popular DQN algorithm and significantly adapted to the specific algorithmic trading problem at hand. The training of the resulting reinforcement learning (RL) agent is entirely based on the generation of artificial trajectories from a limited set of stock market historical data. In order to objectively assess the performance of trading strategies, the research paper also proposes a novel, more rigorous performance assessment methodology. Following this new performance assessment approach, promising results are reported for the TDQN strategy.

Nicolas Vecoven, Damien Ernst, Antoine Wehenkel et al.

Animals excel at adapting their intentions, attention, and actions to the environment, making them remarkably efficient at interacting with a rich, unpredictable and ever-changing external world, a property that intelligent machines currently lack. Such an adaptation property relies heavily on cellular neuromodulation, the biological mechanism that dynamically controls intrinsic properties of neurons and their response to external stimuli in a context-dependent manner. In this paper, we take inspiration from cellular neuromodulation to construct a new deep neural network architecture that is specifically designed to learn adaptive behaviours. The network adaptation capabilities are tested on navigation benchmarks in a meta-reinforcement learning context and compared with state-of-the-art approaches. Results show that neuromodulation is capable of adapting an agent to different tasks and that neuromodulation-based approaches provide a promising way of improving adaptation of artificial systems.

Vincent Francois-Lavet, Guillaume Rabusseau, Joelle Pineau et al.

This paper provides an analysis of the tradeoff between asymptotic bias (suboptimality with unlimited data) and overfitting (additional suboptimality due to limited data) in the context of reinforcement learning with partial observability. Our theoretical analysis formally characterizes that while potentially increasing the asymptotic bias, a smaller state representation decreases the risk of overfitting. This analysis relies on expressing the quality of a state representation by bounding L1 error terms of the associated belief states. Theoretical results are empirically illustrated when the state representation is a truncated history of observations, both on synthetic POMDPs and on a large-scale POMDP in the context of smartgrids, with real-world data. Finally, similarly to known results in the fully observable setting, we also briefly discuss and empirically illustrate how using function approximators and adapting the discount factor may enhance the tradeoff between asymptotic bias and overfitting in the partially observable context.

Aivar Sootla, Damien Ernst

In applications, such as biomedicine and systems/synthetic biology, technical limitations in actuation complicate implementation of time-varying control signals. In order to alleviate some of these limitations, it may be desirable to derive simple control policies, such as step functions with fixed magnitude and length (or temporal pulses). In this technical note, we further develop a recently proposed pulse-based solution to the convergence problem, i.e., minimizing the convergence time to the target exponentially stable equilibrium, for monotone systems. In particular, we extend this solution to monotone systems with parametric uncertainty. Our solutions also provide worst-case estimates on convergence times. Furthermore, we indicate how our tools can be used for a class of non-monotone systems, and more importantly how these tools can be extended to other control problems. We illustrate our approach on switching under parametric uncertainty and regulation around a saddle point problems in a genetic toggle switch system.

Vincent François-Lavet, Raphael Fonteneau, Damien Ernst

Using deep neural nets as function approximator for reinforcement learning tasks have recently been shown to be very powerful for solving problems approaching real-world complexity. Using these results as a benchmark, we discuss the role that the discount factor may play in the quality of the learning process of a deep Q-network (DQN). When the discount factor progressively increases up to its final value, we empirically show that it is possible to significantly reduce the number of learning steps. When used in conjunction with a varying learning rate, we empirically show that it outperforms original DQN on several experiments. We relate this phenomenon with the instabilities of neural networks when they are used in an approximate Dynamic Programming setting. We also describe the possibility to fall within a local optimum during the learning process, thus connecting our discussion with the exploration/exploitation dilemma.

Antonio Sutera, Arnaud Joly, Vincent François-Lavet et al.

In this work, we propose a simple yet effective solution to the problem of connectome inference in calcium imaging data. The proposed algorithm consists of two steps. First, processing the raw signals to detect neural peak activities. Second, inferring the degree of association between neurons from partial correlation statistics. This paper summarises the methodology that led us to win the Connectomics Challenge, proposes a simplified version of our method, and finally compares our results with respect to other inference methods.

Aivar Sootla, Natalja Strelkowa, Damien Ernst et al.

In this paper, we consider the problem of optimal exogenous control of gene regulatory networks. Our approach consists in adapting an established reinforcement learning algorithm called the fitted Q iteration. This algorithm infers the control law directly from the measurements of the system's response to external control inputs without the use of a mathematical model of the system. The measurement data set can either be collected from wet-lab experiments or artificially created by computer simulations of dynamical models of the system. The algorithm is applicable to a wide range of biological systems due to its ability to deal with nonlinear and stochastic system dynamics. To illustrate the application of the algorithm to a gene regulatory network, the regulation of the toggle switch system is considered. The control objective of this problem is to drive the concentrations of two specific proteins to a target region in the state space.

Tobias Jung, Louis Wehenkel, Damien Ernst et al.

Direct policy search (DPS) and look-ahead tree (LT) policies are two widely used classes of techniques to produce high performance policies for sequential decision-making problems. To make DPS approaches work well, one crucial issue is to select an appropriate space of parameterized policies with respect to the targeted problem. A fundamental issue in LT approaches is that, to take good decisions, such policies must develop very large look-ahead trees which may require excessive online computational resources. In this paper, we propose a new hybrid policy learning scheme that lies at the intersection of DPS and LT, in which the policy is an algorithm that develops a small look-ahead tree in a directed way, guided by a node scoring function that is learned through DPS. The LT-based representation is shown to be a versatile way of representing policies in a DPS scheme, while at the same time, DPS enables to significantly reduce the size of the look-ahead trees that are required to take high-quality decisions. We experimentally compare our method with two other state-of-the-art DPS techniques and four common LT policies on four benchmark domains and show that it combines the advantages of the two techniques from which it originates. In particular, we show that our method: (1) produces overall better performing policies than both pure DPS and pure LT policies, (2) requires a substantially smaller number of policy evaluations than other DPS techniques, (3) is easy to tune and (4) results in policies that are quite robust with respect to perturbations of the initial conditions.

Francis Maes, David Lupien St-Pierre, Damien Ernst

Much current research in AI and games is being devoted to Monte Carlo search (MCS) algorithms. While the quest for a single unified MCS algorithm that would perform well on all problems is of major interest for AI, practitioners often know in advance the problem they want to solve, and spend plenty of time exploiting this knowledge to customize their MCS algorithm in a problem-driven way. We propose an MCS algorithm discovery scheme to perform this in an automatic and reproducible way. We first introduce a grammar over MCS algorithms that enables inducing a rich space of candidate algorithms. Afterwards, we search in this space for the algorithm that performs best on average for a given distribution of training problems. We rely on multi-armed bandits to approximately solve this optimization problem. The experiments, generated on three different domains, show that our approach enables discovering algorithms that outperform several well-known MCS algorithms such as Upper Confidence bounds applied to Trees and Nested Monte Carlo search. We also show that the discovered algorithms are generally quite robust with respect to changes in the distribution over the training problems.

Sebastien Bubeck, Damien Ernst, Aurelien Garivier

We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and on the Good-Turing missing mass estimator. We prove two different regret bounds on the performance of this algorithm under weak assumptions on the probabilistic experts. Under more restrictive hypotheses, we also prove a macroscopic optimality result, comparing the algorithm both with an oracle strategy and with uniform sampling. Finally, we provide numerical experiments illustrating these theoretical findings.

Francis Maes, Damien Ernst, Louis Wehenkel

The exploration/exploitation (E/E) dilemma arises naturally in many subfields of Science. Multi-armed bandit problems formalize this dilemma in its canonical form. Most current research in this field focuses on generic solutions that can be applied to a wide range of problems. However, in practice, it is often the case that a form of prior information is available about the specific class of target problems. Prior knowledge is rarely used in current solutions due to the lack of a systematic approach to incorporate it into the E/E strategy. To address a specific class of E/E problems, we propose to proceed in three steps: (i) model prior knowledge in the form of a probability distribution over the target class of E/E problems; (ii) choose a large hypothesis space of candidate E/E strategies; and (iii), solve an optimization problem to find a candidate E/E strategy of maximal average performance over a sample of problems drawn from the prior distribution. We illustrate this meta-learning approach with two different hypothesis spaces: one where E/E strategies are numerically parameterized and another where E/E strategies are represented as small symbolic formulas. We propose appropriate optimization algorithms for both cases. Our experiments, with two-armed Bernoulli bandit problems and various playing budgets, show that the meta-learnt E/E strategies outperform generic strategies of the literature (UCB1, UCB1-Tuned, UCB-v, KL-UCB and epsilon greedy); they also evaluate the robustness of the learnt E/E strategies, by tests carried out on arms whose rewards follow a truncated Gaussian distribution.