Model predictive control (MPC) is a popular approach for trajectory optimization in practical robotics applications. MPC policies can optimize trajectory parameters under kinodynamic and safety constraints and provide guarantees on safety, optimality, generalizability, interpretability, and explainability. However, some behaviors are complex and it is difficult to hand-craft an MPC objective function. A special class of MPC policies called Learnable-MPC addresses this difficulty using imitation learning from expert demonstrations. However, they require the demonstrator and the imitator agents to be identical which is hard to satisfy in many real world applications of robotics. In this paper, we address the practical problem of training Learnable-MPC policies when the demonstrator and the imitator do not share the same dynamics and their state spaces may have a partial overlap. We propose a novel approach that uses a generative adversarial network (GAN) to minimize the Jensen-Shannon divergence between the state-trajectory distributions of the demonstrator and the imitator. We evaluate our approach on a variety of simulated robotics tasks of DeepMind Control suite and demonstrate the efficacy of our approach at learning the demonstrator's behavior without having to copy their actions.
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Price discrimination, which refers to the strategy of setting different prices for different customer groups, has been widely used in online retailing. Although it helps boost the collected revenue for online retailers, it might create serious concerns about fairness, which even violates the regulation and laws. This paper studies the problem of dynamic discriminatory pricing under fairness constraints. In particular, we consider a finite selling horizon of length $T$ for a single product with two groups of customers. Each group of customers has its unknown demand function that needs to be learned. For each selling period, the seller determines the price for each group and observes their purchase behavior. While existing literature mainly focuses on maximizing revenue, ensuring fairness among different customers has not been fully explored in the dynamic pricing literature. This work adopts the fairness notion from Cohen et al. (2022). For price fairness, we propose an optimal dynamic pricing policy regarding regret, which enforces the strict price fairness constraint. In contrast to the standard $\sqrt{T}$-type regret in online learning, we show that the optimal regret in our case is $\tilde{O}(T^{4/5})$. We further extend our algorithm to a more general notion of fairness, which includes demand fairness as a special case. To handle this general class, we propose a soft fairness constraint and develop a dynamic pricing policy that achieves $\tilde{O}(T^{4/5})$ regret. We also demonstrate that our algorithmic techniques can be adapted to more general scenarios such as fairness among multiple groups of customers.
Autonomous driving and intelligent transportation applications have dramatically increased the demand for high-accuracy and low-latency localization services. While cellular networks are potentially capable of target detection and localization, achieving accurate and reliable positioning faces critical challenges. Particularly, the relatively small radar cross sections (RCS) of moving targets and the high complexity for measurement association give rise to weak echo signals and discrepancies in the measurements. To tackle this issue, we propose a novel approach for multi-target localization by leveraging the controllable signal reflection capabilities of intelligent reflecting surfaces (IRSs). Specifically, IRSs are strategically mounted on the targets (e.g., vehicles and robots), enabling effective association of multiple measurements and facilitating the localization process. We aim to minimize the maximum Cram\'er-Rao lower bound (CRLB) of targets by jointly optimizing the target association, the IRS phase shifts, and the dwell time. However, solving this CRLB optimization problem is non-trivial due to the non-convex objective function and closely coupled variables. For single-target localization, a simplified closed-form expression is presented for the case where base stations (BSs) can be deployed flexibly, and the optimal BS location is derived to provide a lower performance bound of the original problem ...
Non-linear model predictive control (nMPC) is a powerful approach to control complex robots (such as humanoids, quadrupeds, or unmanned aerial manipulators (UAMs)) as it brings important advantages over other existing techniques. The full-body dynamics, along with the prediction capability of the optimal control problem (OCP) solved at the core of the controller, allows to actuate the robot in line with its dynamics. This fact enhances the robot capabilities and allows, e.g., to perform intricate maneuvers at high dynamics while optimizing the amount of energy used. Despite the many similarities between humanoids or quadrupeds and UAMs, full-body torque-level nMPC has rarely been applied to UAMs. This paper provides a thorough description of how to use such techniques in the field of aerial manipulation. We give a detailed explanation of the different parts involved in the OCP, from the UAM dynamical model to the residuals in the cost function. We develop and compare three different nMPC controllers: Weighted MPC, Rail MPC, and Carrot MPC, which differ on the structure of their OCPs and on how these are updated at every time step. To validate the proposed framework, we present a wide variety of simulated case studies. First, we evaluate the trajectory generation problem, i.e., optimal control problems solved offline, involving different kinds of motions (e.g., aggressive maneuvers or contact locomotion) for different types of UAMs. Then, we assess the performance of the three nMPC controllers, i.e., closed-loop controllers solved online, through a variety of realistic simulations. For the benefit of the community, we have made available the source code related to this work.
We propose a theoretical framework for studying the imitation of stochastic, non-Markovian, potentially multi-modal (i.e. "complex" ) expert demonstrations in nonlinear dynamical systems. Our framework invokes low-level controllers - either learned or implicit in position-command control - to stabilize imitation policies around expert demonstrations. We show that with (a) a suitable low-level stability guarantee and (b) a stochastic continuity property of the learned policy we call "total variation continuity" (TVC), an imitator that accurately estimates actions on the demonstrator's state distribution closely matches the demonstrator's distribution over entire trajectories. We then show that TVC can be ensured with minimal degradation of accuracy by combining a popular data-augmentation regimen with a novel algorithmic trick: adding augmentation noise at execution time. We instantiate our guarantees for policies parameterized by diffusion models and prove that if the learner accurately estimates the score of the (noise-augmented) expert policy, then the distribution of imitator trajectories is close to the demonstrator distribution in a natural optimal transport distance. Our analysis constructs intricate couplings between noise-augmented trajectories, a technique that may be of independent interest. We conclude by empirically validating our algorithmic recommendations.
Empirical Bayes shrinkage methods usually maintain a prior independence assumption: The unknown parameters of interest are independent from the known precision of the estimates. This assumption is theoretically questionable and empirically rejected, and imposing it inappropriately may harm the performance of empirical Bayes methods. We instead model the conditional distribution of the parameter given the standard errors as a location-scale family, leading to a family of methods that we call CLOSE. We establish that (i) CLOSE is rate-optimal for squared error Bayes regret, (ii) squared error regret control is sufficient for an important class of economic decision problems, and (iii) CLOSE is worst-case robust. We use our method to select high-mobility Census tracts targeting a variety of economic mobility measures in the Opportunity Atlas (Chetty et al., 2020; Bergman et al., 2023). Census tracts selected by close are more mobile on average than those selected by the standard shrinkage method. For 6 out of 15 mobility measures considered, the gain of close over the standard shrinkage method is larger than the gain of the standard method over selecting Census tracts uniformly at random.
Generative Adversarial Networks (GAN) have emerged as a formidable AI tool to generate realistic outputs based on training datasets. However, the challenge of exerting control over the generation process of GANs remains a significant hurdle. In this paper, we propose a novel methodology to address this issue by integrating a reinforcement learning (RL) agent with a latent-space GAN (l-GAN), thereby facilitating the generation of desired outputs. More specifically, we have developed an actor-critic RL agent with a meticulously designed reward policy, enabling it to acquire proficiency in navigating the latent space of the l-GAN and generating outputs based on specified tasks. To substantiate the efficacy of our approach, we have conducted a series of experiments employing the MNIST dataset, including arithmetic addition as an illustrative task. The outcomes of these experiments serve to validate our methodology. Our pioneering integration of an RL agent with a GAN model represents a novel advancement, holding great potential for enhancing generative networks in the future.
The core challenge of offline reinforcement learning (RL) is dealing with the (potentially catastrophic) extrapolation error induced by the distribution shift between the history dataset and the desired policy. A large portion of prior work tackles this challenge by implicitly/explicitly regularizing the learning policy towards the behavior policy, which is hard to estimate reliably in practice. In this work, we propose to regularize towards the Q-function of the behavior policy instead of the behavior policy itself, under the premise that the Q-function can be estimated more reliably and easily by a SARSA-style estimate and handles the extrapolation error more straightforwardly. We propose two algorithms taking advantage of the estimated Q-function through regularizations, and demonstrate they exhibit strong performance on the D4RL benchmarks.
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.
While existing work in robust deep learning has focused on small pixel-level $\ell_p$ norm-based perturbations, this may not account for perturbations encountered in several real world settings. In many such cases although test data might not be available, broad specifications about the types of perturbations (such as an unknown degree of rotation) may be known. We consider a setup where robustness is expected over an unseen test domain that is not i.i.d. but deviates from the training domain. While this deviation may not be exactly known, its broad characterization is specified a priori, in terms of attributes. We propose an adversarial training approach which learns to generate new samples so as to maximize exposure of the classifier to the attributes-space, without having access to the data from the test domain. Our adversarial training solves a min-max optimization problem, with the inner maximization generating adversarial perturbations, and the outer minimization finding model parameters by optimizing the loss on adversarial perturbations generated from the inner maximization. We demonstrate the applicability of our approach on three types of naturally occurring perturbations -- object-related shifts, geometric transformations, and common image corruptions. Our approach enables deep neural networks to be robust against a wide range of naturally occurring perturbations. We demonstrate the usefulness of the proposed approach by showing the robustness gains of deep neural networks trained using our adversarial training on MNIST, CIFAR-10, and a new variant of the CLEVR dataset.
Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.
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