Robustness against adversarial attacks and distribution shifts is a long-standing goal of Reinforcement Learning (RL). To this end, Robust Adversarial Reinforcement Learning (RARL) trains a protagonist against destabilizing forces exercised by an adversary in a competitive zero-sum Markov game, whose optimal solution, i.e., rational strategy, corresponds to a Nash equilibrium. However, finding Nash equilibria requires facing complex saddle point optimization problems, which can be prohibitive to solve, especially for high-dimensional control. In this paper, we propose a novel approach for adversarial RL based on entropy regularization to ease the complexity of the saddle point optimization problem. We show that the solution of this entropy-regularized problem corresponds to a Quantal Response Equilibrium (QRE), a generalization of Nash equilibria that accounts for bounded rationality, i.e., agents sometimes play random actions instead of optimal ones. Crucially, the connection between the entropy-regularized objective and QRE enables free modulation of the rationality of the agents by simply tuning the temperature coefficient. We leverage this insight to propose our novel algorithm, Quantal Adversarial RL (QARL), which gradually increases the rationality of the adversary in a curriculum fashion until it is fully rational, easing the complexity of the optimization problem while retaining robustness. We provide extensive evidence of QARL outperforming RARL and recent baselines across several MuJoCo locomotion and navigation problems in overall performance and robustness.

Self-driving vehicles (SDVs) must be rigorously tested on a wide range of scenarios to ensure safe deployment. The industry typically relies on closed-loop simulation to evaluate how the SDV interacts on a corpus of synthetic and real scenarios and verify it performs properly. However, they primarily only test the system's motion planning module, and only consider behavior variations. It is key to evaluate the full autonomy system in closed-loop, and to understand how variations in sensor data based on scene appearance, such as the shape of actors, affect system performance. In this paper, we propose a framework, Adv3D, that takes real world scenarios and performs closed-loop sensor simulation to evaluate autonomy performance, and finds vehicle shapes that make the scenario more challenging, resulting in autonomy failures and uncomfortable SDV maneuvers. Unlike prior works that add contrived adversarial shapes to vehicle roof-tops or roadside to harm perception only, we optimize a low-dimensional shape representation to modify the vehicle shape itself in a realistic manner to degrade autonomy performance (e.g., perception, prediction, and motion planning). Moreover, we find that the shape variations found with Adv3D optimized in closed-loop are much more effective than those in open-loop, demonstrating the importance of finding scene appearance variations that affect autonomy in the interactive setting.

Minimum Snap Trajectory Generation and Control for an Under-actuated Flapping Wing Aerial VehicleThis paper presents both the trajectory generation and tracking control strategies for an underactuated flapping wing aerial vehicle (FWAV). First, the FWAV dynamics is analyzed in a practical perspective. Then, based on these analyses, we demonstrate the differential flatness of the FWAV system, and develop a general-purpose trajectory generation strategy. Subsequently, the trajectory tracking controller is developed with the help of robust control and switch control techniques. After that, the overall system asymptotic stability is guaranteed by Lyapunov stability analysis. To make the controller applicable in real flight, we also provide several instructions. Finally, a series of experiment results manifest the successful implementation of the proposed trajectory generation strategy and tracking control strategy. This work firstly achieves the closed-loop integration of trajectory generation and control for real 3-dimensional flight of an underactuated FWAV to a practical level.

We study the game modification problem, where a benevolent game designer or a malevolent adversary modifies the reward function of a zero-sum Markov game so that a target deterministic or stochastic policy profile becomes the unique Markov perfect Nash equilibrium and has a value within a target range, in a way that minimizes the modification cost. We characterize the set of policy profiles that can be installed as the unique equilibrium of some game, and establish sufficient and necessary conditions for successful installation. We propose an efficient algorithm, which solves a convex optimization problem with linear constraints and then performs random perturbation, to obtain a modification plan with a near-optimal cost.

Restricting the variance of a policy's return is a popular choice in risk-averse Reinforcement Learning (RL) due to its clear mathematical definition and easy interpretability. Traditional methods directly restrict the total return variance. Recent methods restrict the per-step reward variance as a proxy. We thoroughly examine the limitations of these variance-based methods, such as sensitivity to numerical scale and hindering of policy learning, and propose to use an alternative risk measure, Gini deviation, as a substitute. We study various properties of this new risk measure and derive a policy gradient algorithm to minimize it. Empirical evaluation in domains where risk-aversion can be clearly defined, shows that our algorithm can mitigate the limitations of variance-based risk measures and achieves high return with low risk in terms of variance and Gini deviation when others fail to learn a reasonable policy.

The popularity of bi-level optimization (BO) in deep learning has spurred a growing interest in studying gradient-based BO algorithms. However, existing algorithms involve two coupled learning rates that can be affected by approximation errors when computing hypergradients, making careful fine-tuning necessary to ensure fast convergence. To alleviate this issue, we investigate the use of recently proposed adaptive step-size methods, namely stochastic line search (SLS) and stochastic Polyak step size (SPS), for computing both the upper and lower-level learning rates. First, we revisit the use of SLS and SPS in single-level optimization without the additional interpolation condition that is typically assumed in prior works. For such settings, we investigate new variants of SLS and SPS that improve upon existing suggestions in the literature and are simpler to implement. Importantly, these two variants can be seen as special instances of general family of methods with an envelope-type step-size. This unified envelope strategy allows for the extension of the algorithms and their convergence guarantees to BO settings. Finally, our extensive experiments demonstrate that the new algorithms, which are available in both SGD and Adam versions, can find large learning rates with minimal tuning and converge faster than corresponding vanilla SGD or Adam BO algorithms that require fine-tuning.

We study the contextual bandits with knapsack (CBwK) problem under the high-dimensional setting where the dimension of the feature is large. The reward of pulling each arm equals the multiplication of a sparse high-dimensional weight vector and the feature of the current arrival, with additional random noise. In this paper, we investigate how to exploit this sparsity structure to achieve improved regret for the CBwK problem. To this end, we first develop an online variant of the hard thresholding algorithm that performs the sparse estimation in an online manner. We further combine our online estimator with a primal-dual framework, where we assign a dual variable to each knapsack constraint and utilize an online learning algorithm to update the dual variable, thereby controlling the consumption of the knapsack capacity. We show that this integrated approach allows us to achieve a sublinear regret that depends logarithmically on the feature dimension, thus improving the polynomial dependency established in the previous literature. We also apply our framework to the high-dimension contextual bandit problem without the knapsack constraint and achieve optimal regret in both the data-poor regime and the data-rich regime. We finally conduct numerical experiments to show the efficient empirical performance of our algorithms under the high dimensional setting.

We study gradient flow on the multi-index regression problem for high-dimensional Gaussian data. Multi-index functions consist of a composition of an unknown low-rank linear projection and an arbitrary unknown, low-dimensional link function. As such, they constitute a natural template for feature learning in neural networks. We consider a two-timescale algorithm, whereby the low-dimensional link function is learnt with a non-parametric model infinitely faster than the subspace parametrizing the low-rank projection. By appropriately exploiting the matrix semigroup structure arising over the subspace correlation matrices, we establish global convergence of the resulting Grassmannian population gradient flow dynamics, and provide a quantitative description of its associated `saddle-to-saddle' dynamics. Notably, the timescales associated with each saddle can be explicitly characterized in terms of an appropriate Hermite decomposition of the target link function. In contrast with these positive results, we also show that the related \emph{planted} problem, where the link function is known and fixed, in fact has a rough optimization landscape, in which gradient flow dynamics might get trapped with high probability.

Many crucial scientific problems involve designing novel molecules with desired properties, which can be formulated as a black-box optimization problem over the discrete chemical space. In practice, multiple conflicting objectives and costly evaluations (e.g., wet-lab experiments) make the diversity of candidates paramount. Computational methods have achieved initial success but still struggle with considering diversity in both objective and search space. To fill this gap, we propose a multi-objective Bayesian optimization (MOBO) algorithm leveraging the hypernetwork-based GFlowNets (HN-GFN) as an acquisition function optimizer, with the purpose of sampling a diverse batch of candidate molecular graphs from an approximate Pareto front. Using a single preference-conditioned hypernetwork, HN-GFN learns to explore various trade-offs between objectives. We further propose a hindsight-like off-policy strategy to share high-performing molecules among different preferences in order to speed up learning for HN-GFN. We empirically illustrate that HN-GFN has adequate capacity to generalize over preferences. Moreover, experiments in various real-world MOBO settings demonstrate that our framework predominantly outperforms existing methods in terms of candidate quality and sample efficiency.

The goal of this paper is to demonstrate that common noise may serve as an exploration noise for learning the solution of a mean field game. This concept is here exemplified through a toy linear-quadratic model, for which a suitable form of common noise has already been proven to restore existence and uniqueness. We here go one step further and prove that the same form of common noise may force the convergence of the learning algorithm called `fictitious play', and this without any further potential or monotone structure. Several numerical examples are provided in order to support our theoretical analysis.