Reinforcement learning (RL) has achieved promising results on most robotic control tasks. Safety of learning-based controllers is an essential notion of ensuring the effectiveness of the controllers. Current methods adopt whole consistency constraints during the training, thus resulting in inefficient exploration in the early stage. In this paper, we propose an algorithm named Constrained Policy Optimization with Extra Safety Budget (ESB-CPO) to strike a balance between the exploration efficiency and the constraints satisfaction. In the early stage, our method loosens the practical constraints of unsafe transitions (adding extra safety budget) with the aid of a new metric we propose. With the training process, the constraints in our optimization problem become tighter. Meanwhile, theoretical analysis and practical experiments demonstrate that our method gradually meets the cost limit's demand in the final training stage. When evaluated on Safety-Gym and Bullet-Safety-Gym benchmarks, our method has shown its advantages over baseline algorithms in terms of safety and optimality. Remarkably, our method gains remarkable performance improvement under the same cost limit compared with baselines.

Traditional machine learning paradigms are based on the assumption that both training and test data follow the same statistical pattern, which is mathematically referred to as Independent and Identically Distributed ($i.i.d.$). However, in real-world applications, this $i.i.d.$ assumption often fails to hold due to unforeseen distributional shifts, leading to considerable degradation in model performance upon deployment. This observed discrepancy indicates the significance of investigating the Out-of-Distribution (OOD) generalization problem. OOD generalization is an emerging topic of machine learning research that focuses on complex scenarios wherein the distributions of the test data differ from those of the training data. This paper represents the first comprehensive, systematic review of OOD generalization, encompassing a spectrum of aspects from problem definition, methodological development, and evaluation procedures, to the implications and future directions of the field. Our discussion begins with a precise, formal characterization of the OOD generalization problem. Following that, we categorize existing methodologies into three segments: unsupervised representation learning, supervised model learning, and optimization, according to their positions within the overarching learning process. We provide an in-depth discussion on representative methodologies for each category, further elucidating the theoretical links between them. Subsequently, we outline the prevailing benchmark datasets employed in OOD generalization studies. To conclude, we overview the existing body of work in this domain and suggest potential avenues for future research on OOD generalization. A summary of the OOD generalization methodologies surveyed in this paper can be accessed at http://out-of-distribution-generalization.com.

The control of free-floating robots requires dealing with several challenges. The motion of such robots evolves on a continuous manifold described by the Special Euclidean Group of dimension 3, known as SE(3). Methods from finite horizon Linear Quadratic Regulators (LQR) control have gained recent traction in the robotics community. However, such approaches are inherently solving an unconstrained optimization problem and hence are unable to respect the manifold constraints imposed by the group structure of SE(3). This may lead to small errors, singularity problems and double cover issues depending on the choice of coordinates to model the floating base motion. In this paper, we propose the use of canonical exponential coordinates of SE(3) and the associated Exponential map along with its differentials to embed this structure in the theory of finite horizon LQR controllers.

In this paper, we introduce a novel open source toolbox for design optimization in Soft Robotics. We consider that design optimization is an important trend in Soft Robotics that is changing the way in which designs will be shared and adopted. We evaluate this toolbox on the example of a cable-driven, sensorized soft finger. For devices like these, that feature both actuation and sensing, the need for multi-objective optimization capabilities naturally arises, because at the very least, a trade-off between these two aspects has to be found. Thus, multi-objective optimization capability is one of the central features of the proposed toolbox. We evaluate the optimization of the soft finger and show that extreme points of the optimization trade-off between sensing and actuation are indeed far apart on actually fabricated devices for the established metrics. Furthermore, we provide an in depth analysis of the sim-to-real behavior of the example, taking into account factors such as the mesh density in the simulation, mechanical parameters and fabrication tolerances.

Time-varying pricing tariffs incentivize consumers to shift their electricity demand and reduce costs, but may increase the energy burden for consumers with limited response capability. The utility must thus balance affordability and response incentives when designing these tariffs by considering consumers' response expectations. This paper proposes a joint learning-based identification and optimization method to design equitable time-varying tariffs. Our proposed method encodes historical prices and demand response data into a recurrent neural network (RNN) to capture high-dimensional and non-linear consumer price response behaviors. We then embed the RNN into the tariff design optimization, formulating a non-linear optimization problem with a quadratic objective. We propose a gradient-based solution method that achieves fast and scalable computation. Simulation using real-world consumer data shows that our equitable tariffs protect low-income consumers from price surges while effectively motivating consumers to reduce peak demand. The method also ensures revenue recovery for the utility company and achieves robust performance against demand response uncertainties and prediction errors.

Recent work suggests that interpolating between the weights of two specialized language models can transfer knowledge between tasks in a way that multi-task learning cannot. However, very few have explored interpolation between more than two models, where each has a distinct knowledge base. In this paper, we introduce Derivative Free Weight-space Ensembling (DFWE), a new few-sample task transfer approach for open-domain dialogue. Our framework creates a set of diverse expert language models trained using a predefined set of source tasks. Next, we finetune each of the expert models on the target task, approaching the target task from several distinct knowledge bases. Finally, we linearly interpolate between the model weights using a gradient-free-optimization algorithm, to efficiently find a good interpolation weighting. We demonstrate the effectiveness of the method on FETA-Friends outperforming the standard pretrain-finetune approach.

Nonconvex-nonconcave minimax optimization has gained widespread interest over the last decade. However, most existing works focus on variants of gradient descent-ascent (GDA) algorithms, which are only applicable to smooth nonconvex-concave settings. To address this limitation, we propose a novel algorithm named smoothed proximal linear descent-ascent (smoothed PLDA), which can effectively handle a broad range of structured nonsmooth nonconvex-nonconcave minimax problems. Specifically, we consider the setting where the primal function has a nonsmooth composite structure and the dual function possesses the Kurdyka-Lojasiewicz (KL) property with exponent $\theta \in [0,1)$. We introduce a novel convergence analysis framework for smoothed PLDA, the key components of which are our newly developed nonsmooth primal error bound and dual error bound. Using this framework, we show that smoothed PLDA can find both $\epsilon$-game-stationary points and $\epsilon$-optimization-stationary points of the problems of interest in $\mathcal{O}(\epsilon^{-2\max\{2\theta,1\}})$ iterations. Furthermore, when $\theta \in [0,\frac{1}{2}]$, smoothed PLDA achieves the optimal iteration complexity of $\mathcal{O}(\epsilon^{-2})$. To further demonstrate the effectiveness and wide applicability of our analysis framework, we show that certain max-structured problem possesses the KL property with exponent $\theta=0$ under mild assumptions. As a by-product, we establish algorithm-independent quantitative relationships among various stationarity concepts, which may be of independent interest.

While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based problems. To overcome the lack of permutation-based benchmark problems, we propose a general way to transfer the classic pseudo-Boolean benchmarks into benchmarks defined on sets of permutations. We then conduct a rigorous runtime analysis of the permutation-based $(1+1)$ EA proposed by Scharnow, Tinnefeld, and Wegener (2004) on the analogues of the LeadingOnes and Jump benchmarks. The latter shows that, different from bit-strings, it is not only the Hamming distance that determines how difficult it is to mutate a permutation $\sigma$ into another one $\tau$, but also the precise cycle structure of $\sigma \tau^{-1}$. For this reason, we also regard the more symmetric scramble mutation operator. We observe that it not only leads to simpler proofs, but also reduces the runtime on jump functions with odd jump size by a factor of $\Theta(n)$. Finally, we show that a heavy-tailed version of the scramble operator, as in the bit-string case, leads to a speed-up of order $m^{\Theta(m)}$ on jump functions with jump size $m$. A short empirical analysis confirms these findings, but also reveals that small implementation details like the rate of void mutations can make an important difference.

In the paper, we propose an effective and efficient Compositional Federated Learning (ComFedL) algorithm for solving a new compositional Federated Learning (FL) framework, which frequently appears in many data mining and machine learning problems with a hierarchical structure such as distributionally robust FL and model-agnostic meta learning (MAML). Moreover, we study the convergence analysis of our ComFedL algorithm under some mild conditions, and prove that it achieves a convergence rate of $O(\frac{1}{\sqrt{T}})$, where $T$ denotes the number of iteration. To the best of our knowledge, our new Compositional FL framework is the first work to bridge federated learning with composition stochastic optimization. In particular, we first transform the distributionally robust FL (i.e., a minimax optimization problem) into a simple composition optimization problem by using KL divergence regularization. At the same time, we also first transform the distribution-agnostic MAML problem (i.e., a minimax optimization problem) into a simple yet effective composition optimization problem. Finally, we apply two popular machine learning tasks, i.e., distributionally robust FL and MAML to demonstrate the effectiveness of our algorithm.

We address the theoretical and practical problems related to the trajectory generation and tracking control of tail-sitter UAVs. Theoretically, we focus on the differential flatness property with full exploitation of actual UAV aerodynamic models, which lays a foundation for generating dynamically feasible trajectory and achieving high-performance tracking control. We have found that a tail-sitter is differentially flat with accurate aerodynamic models within the entire flight envelope, by specifying coordinate flight condition and choosing the vehicle position as the flat output. This fundamental property allows us to fully exploit the high-fidelity aerodynamic models in the trajectory planning and tracking control to achieve accurate tail-sitter flights. Particularly, an optimization-based trajectory planner for tail-sitters is proposed to design high-quality, smooth trajectories with consideration of kinodynamic constraints, singularity-free constraints and actuator saturation. The planned trajectory of flat output is transformed to state trajectory in real-time with consideration of wind in environments. To track the state trajectory, a global, singularity-free, and minimally-parameterized on-manifold MPC is developed, which fully leverages the accurate aerodynamic model to achieve high-accuracy trajectory tracking within the whole flight envelope. The effectiveness of the proposed framework is demonstrated through extensive real-world experiments in both indoor and outdoor field tests, including agile SE(3) flight through consecutive narrow windows requiring specific attitude and with speed up to 10m/s, typical tail-sitter maneuvers (transition, level flight and loiter) with speed up to 20m/s, and extremely aggressive aerobatic maneuvers (Wingover, Loop, Vertical Eight and Cuban Eight) with acceleration up to 2.5g.