Reinforcement Learning has drawn huge interest as a tool for solving optimal control problems. Solving a given problem (task or environment) involves converging towards an optimal policy. However, there might exist multiple optimal policies that can dramatically differ in their behaviour; for example, some may be faster than the others but at the expense of greater risk. We consider and study a distribution of optimal policies. We design a curiosity-augmented Metropolis algorithm (CAMEO), such that we can sample optimal policies, and such that these policies effectively adopt diverse behaviours, since this implies greater coverage of the different possible optimal policies. In experimental simulations we show that CAMEO indeed obtains policies that all solve classic control problems, and even in the challenging case of environments that provide sparse rewards. We further show that the different policies we sample present different risk profiles, corresponding to interesting practical applications in interpretability, and represents a first step towards learning the distribution of optimal policies itself.
相關內容
Structure learning via MCMC sampling is known to be very challenging because of the enormous search space and the existence of Markov equivalent DAGs. Theoretical results on the mixing behavior are lacking. In this work, we prove the rapid mixing of a random walk Metropolis-Hastings algorithm, which reveals that the complexity of Bayesian learning of sparse equivalence classes grows only polynomially in $n$ and $p$, under some high-dimensional assumptions. A series of high-dimensional consistency results is obtained, including the strong selection consistency of an empirical Bayes model for structure learning. Our proof is based on two new results. First, we derive a general mixing time bound on finite state spaces, which can be applied to local MCMC schemes for other model selection problems. Second, we construct high-probability search paths on the space of equivalence classes with node degree constraints by proving a combinatorial property of DAG comparisons. Simulation studies on the proposed MCMC sampler are conducted to illustrate the main theoretical findings.
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a natural remedy is to judiciously select a good sample of units, for which the responses are to be evaluated. In this paper, we adopt the classical criteria in design of experiments to quantify the information of a given sample regarding parameter estimation. Then, we provide a theoretical justification for approximating the optimal sample problem by a continuous problem, for which fast algorithms can be further developed with the guarantee of global convergence. Our results have the following novelties: (i) The statistical efficiency of any candidate sample can be evaluated without knowing the exact optimal sample; (ii) It can be applied to a very wide class of statistical models; (iii) It can be integrated with a broad class of information criteria; (iv) It is much faster than existing algorithms. $(v)$ A geometric interpretation is adopted to theoretically justify the relaxation of the original combinatorial problem to continuous optimization problem.
Optimization of experimental materials synthesis and characterization through active learning methods has been growing over the last decade, with examples ranging from measurements of diffraction on combinatorial alloys at synchrotrons, to searches through chemical space with automated synthesis robots for perovskites. In virtually all cases, the target property of interest for optimization is defined apriori with limited human feedback during operation. In contrast, here we present the development of a new type of human in the loop experimental workflow, via a Bayesian optimized active recommender system (BOARS), to shape targets on the fly, employing human feedback. We showcase examples of this framework applied to pre-acquired piezoresponse force spectroscopy of a ferroelectric thin film, and then implement this in real time on an atomic force microscope, where the optimization proceeds to find symmetric piezoresponse amplitude hysteresis loops. It is found that such features appear more affected by subsurface defects than the local domain structure. This work shows the utility of human-augmented machine learning approaches for curiosity-driven exploration of systems across experimental domains. The analysis reported here is summarized in Colab Notebook for the purpose of tutorial and application to other data: //github.com/arpanbiswas52/varTBO
Studying causal effects of continuous treatments is important for gaining a deeper understanding of many interventions, policies, or medications, yet researchers are often left with observational studies for doing so. In the observational setting, confounding is a barrier to the estimation of causal effects. Weighting approaches seek to control for confounding by reweighting samples so that confounders are comparable across different treatment values. Yet, for continuous treatments, weighting methods are highly sensitive to model misspecification. In this paper we elucidate the key property that makes weights effective in estimating causal quantities involving continuous treatments. We show that to eliminate confounding, weights should make treatment and confounders independent on the weighted scale. We develop a measure that characterizes the degree to which a set of weights induces such independence. Further, we propose a new model-free method for weight estimation by optimizing our measure. We study the theoretical properties of our measure and our weights, and prove that our weights can explicitly mitigate treatment-confounder dependence. The empirical effectiveness of our approach is demonstrated in a suite of challenging numerical experiments, where we find that our weights are quite robust and work well under a broad range of settings.
We consider the classic 1-center problem: Given a set $P$ of $n$ points in a metric space find the point in $P$ that minimizes the maximum distance to the other points of $P$. We study the complexity of this problem in $d$-dimensional $\ell_p$-metrics and in edit and Ulam metrics over strings of length $d$. Our results for the 1-center problem may be classified based on $d$ as follows. $\bullet$ Small $d$: Assuming the hitting set conjecture (HSC), we show that when $d=\omega(\log n)$, no subquadratic algorithm can solve 1-center problem in any of the $\ell_p$-metrics, or in edit or Ulam metrics. $\bullet$ Large $d$: When $d=\Omega(n)$, we extend our conditional lower bound to rule out subquartic algorithms for 1-center problem in edit metric (assuming Quantified SETH). On the other hand, we give a $(1+\epsilon)$-approximation for 1-center in Ulam metric with running time $\tilde{O_{\varepsilon}}(nd+n^2\sqrt{d})$. We also strengthen some of the above lower bounds by allowing approximations or by reducing the dimension $d$, but only against a weaker class of algorithms which list all requisite solutions. Moreover, we extend one of our hardness results to rule out subquartic algorithms for the well-studied 1-median problem in the edit metric, where given a set of $n$ strings each of length $n$, the goal is to find a string in the set that minimizes the sum of the edit distances to the rest of the strings in the set.
There is increasing interest in allocating treatments based on observed individual characteristics: examples include targeted marketing, individualized credit offers, and heterogeneous pricing. Treatment personalization introduces incentives for individuals to modify their behavior to obtain a better treatment. Strategic behavior shifts the joint distribution of covariates and potential outcomes. The optimal rule without strategic behavior allocates treatments only to those with a positive Conditional Average Treatment Effect. With strategic behavior, we show that the optimal rule can involve randomization, allocating treatments with less than 100% probability even to those who respond positively on average to the treatment. We propose a sequential experiment based on Bayesian Optimization that converges to the optimal treatment rule without parametric assumptions on individual strategic behavior.
We introduce a model for multi-agent interaction problems to understand how a heterogeneous team of agents should organize its resources to tackle a heterogeneous team of attackers. This model is inspired by how the human immune system tackles a diverse set of pathogens. The key property of this model is "cross-reactivity" which enables a particular defender type to respond strongly to some attackers but weakly to a few different types of attackers. Due to this, the optimal defender distribution that minimizes the harm incurred by attackers is supported on a discrete set. This allows the defender team to allocate resources to a few types and yet tackle a large number of attacker types. We study this model in different settings to characterize a set of guiding principles for control problems with heterogeneous teams of agents, e.g., sensitivity of the harm to sub-optimal defender distributions, teams consisting of a small number of attackers and defenders, estimating and tackling an evolving attacker distribution, and competition between defenders that gives near-optimal behavior using decentralized computation of the control. We also compare this model with reinforcement-learned policies for the defender team.
Recently, learning-based controllers have been shown to push mobile robotic systems to their limits and provide the robustness needed for many real-world applications. However, only classical optimization-based control frameworks offer the inherent flexibility to be dynamically adjusted during execution by, for example, setting target speeds or actuator limits. We present a framework to overcome this shortcoming of neural controllers by conditioning them on an auxiliary input. This advance is enabled by including a feature-wise linear modulation layer (FiLM). We use model-free reinforcement-learning to train quadrotor control policies for the task of navigating through a sequence of waypoints in minimum time. By conditioning the policy on the maximum available thrust or the viewing direction relative to the next waypoint, a user can regulate the aggressiveness of the quadrotor's flight during deployment. We demonstrate in simulation and in real-world experiments that a single control policy can achieve close to time-optimal flight performance across the entire performance envelope of the robot, reaching up to 60 km/h and 4.5g in acceleration. The ability to guide a learned controller during task execution has implications beyond agile quadrotor flight, as conditioning the control policy on human intent helps safely bringing learning based systems out of the well-defined laboratory environment into the wild.
Federated learning (FL) is a privacy-preserving distributed machine learning paradigm that enables collaborative training among geographically distributed and heterogeneous devices without gathering their data. Extending FL beyond the supervised learning models, federated reinforcement learning (FRL) was proposed to handle sequential decision-making problems in edge computing systems. However, the existing FRL algorithms directly combine model-free RL with FL, thus often leading to high sample complexity and lacking theoretical guarantees. To address the challenges, we propose a novel FRL algorithm that effectively incorporates model-based RL and ensemble knowledge distillation into FL for the first time. Specifically, we utilise FL and knowledge distillation to create an ensemble of dynamics models for clients, and then train the policy by solely using the ensemble model without interacting with the environment. Furthermore, we theoretically prove that the monotonic improvement of the proposed algorithm is guaranteed. The extensive experimental results demonstrate that our algorithm obtains much higher sample efficiency compared to classic model-free FRL algorithms in the challenging continuous control benchmark environments under edge computing settings. The results also highlight the significant impact of heterogeneous client data and local model update steps on the performance of FRL, validating the insights obtained from our theoretical analysis.
When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191