Mixed-Integer Linear Programming (MILP) lies at the core of many real-world combinatorial optimization (CO) problems, traditionally solved by branch-and-bound (B&B). A key driver influencing B&B solvers efficiency is the variable selection heuristic that guides branching decisions. Looking to move beyond static, hand-crafted heuristics, recent work has explored adapting traditional reinforcement learning (RL) algorithms to the B&B setting, aiming to learn branching strategies tailored to specific MILP distributions. In parallel, RL agents have achieved remarkable success in board games, a very specific type of combinatorial problems, by leveraging environment simulators to plan via Monte Carlo Tree Search (MCTS). Building on these developments, we introduce Plan-and-Branch-and-Bound (PlanB&B), a model-based reinforcement learning (MBRL) agent that leverages a learned internal model of the B&B dynamics to discover improved branching strategies. Computational experiments empirically validate our approach, with our MBRL branching agent outperforming previous state-of-the-art RL methods across four standard MILP benchmarks.

In complex control tasks, finding high-performing policies often requires discovering and exploiting specific behavioral strategies. While Quality-Diversity (QD) algorithms can uncover these strategies through extensive behavior space exploration, they sacrifice efficiency by improving suboptimal behaviors. Conversely, Evolution Strategies (ES) achieve impressive performance through focused optimization but frequently become trapped in local optima due to limited behavioral exploration. We present Quality with J ust E nough Di versity (JEDi), a new optimization framework that resolves this fundamental tension. JEDi employs a combination of Gaussian Process modeling and parallel ES to intelligently explore behavioral space while maintaining focused optimization. At its core, JEDi learns a probabilistic mapping between behaviors and performance, using this model to identify and target promising behavioral regions that could unlock better solutions. This targeted exploration is achieved through multiple Evolution Strategy emitters that simultaneously optimize toward selected behaviors while maximizing task performance. To further improve JEDi’s exploration capabilities, we introduce its Dynamic variant DyJEDi with an adaptive restart mechanism that dynamically detects and responds to emitter convergence, independently restarting each Evolution Strategy when it stagnates in both behavior and fitness space. This dynamic approach significantly improves exploration efficiency and robustness to local optima. We demonstrate that DyJEDi outperforms both traditional ES and QD approaches across challenging continuous robotics control tasks, achieving higher final performance. Most notably, DyJEDi solves several hard exploration problems where standard ES methods consistently fail.

Mixed-Integer Linear Programming (MILP) is a powerful framework used to address a wide range of NP-hard combinatorial optimization problems, often solved by Branch and bound (B&B). A key factor influencing the performance of B&B solvers is the variable selection heuristic governing branching decisions. Recent contributions have sought to adapt reinforcement learning (RL) algorithms to the B&B setting to learn optimal branching policies, through Markov Decision Processes (MDP) inspired formulations, and ad hoc convergence theorems and algorithms. In this work, we introduce BBMDP, a principled vanilla MDP formulation for variable selection in B&B, allowing to leverage a broad range of RL algorithms for the purpose of learning optimal B&B heuristics. Computational experiments validate our model empirically, as our branching agent outperforms prior state-of-the-art RL agents on four standard MILP benchmarks.

Evolutionary Algorithms (EA) have been successfully used for the optimization of neural networks for policy search, but they still remain sample inefficient and underperforming in some cases compared to gradient-based reinforcement learning (RL). Various methods combine the two approaches, many of them training a RL algorithm on data from EA evaluations and injecting the RL actor into the EA population. However, when using Evolution Strategies (ES) as the EA, the RL actor can drift genetically far from the the ES distribution and injection can cause a collapse of the ES performance. Here, we highlight the phenomenon of genetic drift where the actor genome and the ES population distribution progressively drift apart, leading to injection having a negative impact on the ES. We introduce Genetic Drift Regularization (GDR)11https://anonymous.4open.science/r/GDR-E784, a simple regularization method in the actor training loss that prevents the actor genome from drifting away from the ES. We show that GDR can improve ES convergence on problems where RL learns well, but also helps RL training on other tasks, fixes the injection issues better than previous controlled injection methods

Evolution Strategies (ES) are effective gradient-free optimization methods that can be competitive with gradient-based approaches for policy search. ES only rely on the total episodic scores of solutions in their population, from which they estimate fitness gradients for their update with no access to true gradient information. However this makes them sensitive to deceptive fitness landscapes, and they tend to only explore one way to solve a problem. Quality-Diversity methods such as MAP-Elites introduced additional information with behavior descriptors (BD) to return a population of diverse solutions, which helps exploration but leads to a large part of the evaluation budget not being focused on finding the best performing solution. Here we show that behavior information can also be leveraged to find the best policy by identifying promising search areas which can then be efficiently explored with ES. We introduce the framework of Quality with Just Enough Diversity (JEDi) which learns the relationship between behavior and fitness to focus evaluations on solutions that matter. When trying to reach higher fitness values, JEDi outperforms both QD and ES methods on hard exploration tasks like mazes and on complex control problems with large policies.

Critical software systems require stringent testing to identify possible failure cases, which can be difficult to find using manual testing. In this study, we report our industrial experience in testing a realistic R&D flight control system using a heuristic based testing method. Our approach utilizes evolutionary strategies augmented with intrinsic motivation to yield a diverse range of test cases, each revealing different potential failure scenarios within the system. This diversity allows for a more comprehensive identification and understanding of the system’s vulnerabilities. We analyze the test cases found by evolution to identify the system’s weaknesses. The results of our study show that our approach can be used to improve the reliability and robustness of avionics systems by providing high-quality test cases in an efficient and cost-effective manner.

The ability to perform different skills can encourage agents to explore. In this work, we aim to construct a set of diverse skills that uniformly cover the state space. We propose a formalization of this search for diverse skills, building on a previous definition based on the mutual information between states and skills. We consider the distribution of states reached by a policy conditioned on each skill and leverage the successor state representation to maximize the difference between these skill distributions. We call this approach LEADS: Learning Diverse Skills through Successor State Representations. We demonstrate our approach on a set of maze navigation and robotic control tasks which show that our method is capable of constructing a diverse set of skills which exhaustively cover the state space without relying on reward or exploration bonuses. Our findings demonstrate that this new formalization promotes more robust and efficient exploration by combining mutual information maximization and exploration bonuses.

Robust reinforcement learning is essential for deploying reinforcement learning algorithms in real-world scenarios where environmental uncertainty predominates. Traditional robust reinforcement learning often depends on rectangularity assumptions, where adverse probability measures of outcome states are assumed to be independent across different states and actions. This assumption, rarely fulfilled in practice, leads to overly conservative policies. To address this problem, we introduce a new time-constrained robust MDP (TC-RMDP) formulation that considers multifactorial, correlated, and time-dependent disturbances, thus more accurately reflecting real-world dynamics. This formulation goes beyond the conventional rectangularity paradigm, offering new perspectives and expanding the analytical framework for robust RL. We propose three distinct algorithms, each using varying levels of environmental information, and evaluate them extensively on continuous control benchmarks. Our results demonstrate that these algorithms yield an efficient tradeoff between performance and robustness, outperforming traditional deep robust RL methods in time-constrained environments while preserving robustness in classical benchmarks. This study revisits the prevailing assumptions in robust RL and opens new avenues for developing more practical and realistic RL applications.

Deep neural networks have demonstrated their ability to automatically extract meaningful features from data. However, in supervised learning, information specific to the dataset used for training, but irrelevant to the task at hand, may remain encoded in the extracted representations. This remaining information introduces a domain-specific bias, weakening the generalization performance. In this work, we propose splitting the information into a task-related representation and its complementary context representation. We propose an original method, combining adversarial feature predictors and cyclic reconstruction, to disentangle these two representations in the single-domain supervised case. We then adapt this method to the unsupervised domain adaptation (UDA) problem, consisting of training a model capable of performing on both a source and a target domain. In particular, our method promotes disentanglement in the target domain, despite the absence of training labels. This enables the isolation of task-specific information from both domains and a projection into a common representation. The task-specific representation allows the efficient transfer of knowledge acquired from the source domain to the target domain. In the single-domain case, we demonstrate the quality of our representations on information retrieval tasks and the generalization benefits induced by sharpened task-specific representations. We then validate the proposed method on several classical domain adaptation (DA) benchmarks and illustrate the benefits of disentanglement for DA.

When searching for policies, reward-sparse environments often lack sufficient information about which behaviors to improve upon or avoid. In such environments, the policy search process is bound to blindly search for reward-yielding transitions and no early reward can bias this search in one direction or another. A way to overcome this is to use intrinsic motivation in order to explore new transitions until a reward is found. In this work, we use a recently proposed definition of intrinsic motivation, Curiosity, in an evolutionary policy search method. We propose Curiosity-ES, 1 an evolutionary strategy adapted to use Curiosity as a fitness metric. We compare Curiosity-ES with other evolutionary algorithms intended for exploration, as well as with Curiosity-based reinforcement learning, and find that Curiosity-ES can generate higher diversity without the need for an explicit diversity criterion and leads to more policies which find reward.

Selection in genetic algorithms is difficult for stochastic problems due to noise in the fitness space. Common methods to deal with this fitness noise include sampling multiple fitness values, which can be expensive. We propose LUCIE, the Lower Upper Confidence Intervals Elitism method, which selects individuals based on confidence. By focusing evaluation on separating promising individuals from others, we demonstrate that LUCIE can be effectively used as an elitism mechanism in genetic algorithms. We provide a theoretical analysis on the convergence of LUCIE and demonstrate its ability to select fit individuals across multiple types of noise on the OneMax and LeadingOnes problems. We also evaluate LUCIE as a selection method for neuroevolution on control policies with stochastic fitness values.

Several algorithms have been proposed to sample non-uniformly the replay buffer of deep Reinforcement Learning (RL) agents to speed-up learning, but very few theoretical foundations of these sampling schemes have been provided. Among others, Prioritized Experience Replay appears as a hyperparameter sensitive heuristic, even though it can provide good performance. In this work, we cast the replay buffer sampling problem as an importance sampling one for estimating the gradient. This allows deriving the theoretically optimal sampling distribution, yielding the best theoretical convergence speed. Elaborating on the knowledge of the ideal sampling scheme, we exhibit new theoretical foundations of Prioritized Experience Replay. The optimal sampling distribution being intractable, we make several approximations providing good results in practice and introduce, among others, LaBER (Large Batch Experience Replay), an easy-to-code and efficient method for sampling the replay buffer. LaBER, which can be combined with Deep Q-Networks, distributional RL agents or actor-critic methods, yields improved performance over a diverse range of Atari games and PyBullet environments, compared to the base agent it is implemented on and to other prioritization schemes.

Deep reinforcement learning policies, despite their outstanding efficiency in simulated visual control tasks, have shown disappointing ability to generalize across disturbances in the input training images. Changes in image statistics or distracting background elements are pitfalls that prevent generalization and real-world applicability of such control policies.We elaborate on the intuition that a good visual policy should be able to identify which pixels are important for its decision, and preserve this identification of important sources of information across images. This implies that training of a policy with small generalization gap should focus on such important pixels and ignore the others. This leads to the introduction of saliency-guided Q-networks (SGQN), a generic method for visual reinforcement learning, that is compatible with any value function learning method. SGQN vastly improves the generalization capability of Soft Actor-Critic agents and outperforms existing state-of-the-art methods on the Deepmind Control Generalization benchmark, setting a new reference in terms of training efficiency, generalization gap, and policy interpretability.

We consider the problem of knowledge transfer when an agent is facing a series of Reinforcement Learning (RL) tasks. We introduce a novel metric between Markov Decision Processes and establish that close MDPs have close optimal value functions. Formally, the optimal value functions are Lipschitz continuous with respect to the tasks space. These theoretical results lead us to a value-transfer method for Lifelong RL, which we use to build a PAC-MDP algorithm with improved convergence rate. Further, we show the method to experience no negative transfer with high probability. We illustrate the benefits of the method in Lifelong RL experiments.

A major limitation to the optimization of artificial neural networks (ANN) with evolutionary methods lies in the high dimensionality of the search space, the number of weights growing quadratically with the size of the network. This leads to expensive training costs, especially in evolution strategies which rely on matrices whose sizes grow with the number of genes. We introduce a geometric encoding for neural network evolution (GENE) as a representation of ANN parameters in a smaller space that scales linearly with the number of neurons, allowing for efficient parameter search. Each neuron of the network is encoded as a point in a latent space and the weight of a connection between two neurons is computed as the distance between them. The coordinates of all neurons are then optimized with evolution strategies in a reduced search space while not limiting network fitness and possibly improving search.

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This work tackles the problem of robust zero-shot planning in non-stationary stochastic environments. We study Markov Decision Processes (MDPs) evolving over time and consider Model-Based Reinforcement Learning algorithms in this setting. We make two hypotheses: 1) the environment evolves continuously with a bounded evolution rate; 2) a current model is known at each decision epoch but not its evolution. Our contribution can be presented in four points. 1) we define a specific class of MDPs that we call Non-Stationary MDPs (NSMDPs). We introduce the notion of regular evolution by making an hypothesis of Lipschitz-Continuity on the transition and reward functions w.r.t. time; 2) we consider a planning agent using the current model of the environment but unaware of its future evolution. This leads us to consider a worst-case method where the environment is seen as an adversarial agent; 3) following this approach, we propose the Risk-Averse Tree-Search (RATS) algorithm, a zero-shot Model-Based method similar to Minimax search; 4) we illustrate the benefits brought by RATS empirically and compare its performance with reference Model-Based algorithms.

In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning in subsequent decision steps by directly using sub-trees as action recommender. Firstly, we propose a method for open loop control via a new algorithm taking the decision of re-planning or not at each time step based on an analysis of the statistics of the sub-tree. Secondly, we show that the probability of selecting a suboptimal action at any depth of the tree can be upper bounded and converges towards zero. Moreover, this upper bound decays in a logarithmic way between subsequent depths. This leads to a distinction between node-wise optimality and state-wise optimality. Finally, we empirically demonstrate that our method achieves a compromise between loss of performance and computational gain.

In this paper a sparse approximation of inference for multi-output Gaussian Process models based on a Variational Inference approach is presented. In Gaussian Processes a multi-output kernel is a covariance function over correlated outputs. Using a general framework for constructing auto- and cross-covariance functions that are consistent with the physical laws, physical relationships among several outputs can be imposed. One major issue with Gaussian Processes is efficient inference, when scaling up-to large datasets. The issue of scaling becomes even more important when dealing with multiple outputs, since the cost of inference increases rapidly with the number of outputs. In this paper we combine the use of variational inference for efficient inference with multi-output kernels enforcing relationships between outputs. Results of the proposed methodology for synthetic data and real world applications are presented. The main contribution of this paper is the application and validation of our methodology on a dataset of real aircraft flight tests, while imposing knowledge of aircraft physics into the model.

The allocation of visual attention is a key factor for the humans when operating complex systems under time pressure with multiple information sources. In some situations, attentional tunneling is likely to appear and leads to excessive focus and poor decision making. In this study, we propose a formal approach to detect the occurrence of such an attentional impairment that is based on machine learning techniques. An experiment was conducted to provoke attentional tunneling during which psycho-physiological and oculomotor data from 23 participants were collected. Data from 18 participants were used to train an adaptive neuro-fuzzy inference system (ANFIS). From a machine learning point of view, the classification performance of the trained ANFIS proved the validity of this approach. Furthermore, the resulting classification rules were consistent with the attentional tunneling literature. Finally, the classifier was robust to detect attentional tunneling when performing over test data from four participants.

We introduce a new plan repair method for problems cast as Mixed Integer Programs. In order to tackle the inherent complexity of these NP-hard problems, our approach relies on the use of Supervised Learning method for the offline construction of a predictor which takes the problem's parameters as input and infers values for the discrete optimization variables. This way, the online resolution time of the plan repair problem can be greatly decreased by avoiding a large part of the combinatorial search among discrete variables. This contribution was motivated by the large-scale problem of intra-daily recourse strategy computation in electrical power systems. We report and discuss results on this benchmark, illustrating the different aspects and mechanisms of this new approach which provided close-to-optimal solutions in only a fraction of the computational time necessary for existing solvers.

We introduce TiMDPpoly, an algorithm designed to solve planning problems with durative actions, under probabilistic uncertainty, in a non-stationary, continuous-time context. Mission planning for autonomous agents such as planetary rovers or unmanned aircrafts often correspond to such time-dependent planning problems. Modeling these problems can be cast through the framework of time-dependent Markov decision processes (TiMDPs). We analyze the TiMDP optimality equations in order to exploit their properties. Then, we focus on the class of piecewise polynomial models in order to approximate TiMDPs, and introduce several algorithmic contributions which lead to the TiMDPpolyalgorithm for TiMDPs. Finally, our approach is evaluated on an unmanned aircraft mission planning problem and on an adapted version of the well-known Mars rover domain.

Time is a crucial variable in planning and often requires special attention since it introduces a specific structure along with additional complexity, especially in the case of decision under uncertainty. In this paper, after reviewing and comparing MDP frameworks designed to deal with temporal problems, we focus on Generalized Semi-Markov Decision Processes (GSMDP) with observable time. We highlight the inherent structure and complexity of these problems and present the differences with classical reinforcement learning problems. Finally, we introduce a new simulation-based reinforcement learning method for solving GSMDP, bringing together results from simulation-based policy iteration, regression techniques and simulation theory. We illustrate our approach on a subway network control example.