arXiv subjects

Aldo Pacchiano

Publications and source records attributed to Aldo Pacchiano.

85 records · Page 5Linked to original sources

arXiv2020

Robustness Guarantees for Mode Estimation with an Application to Bandits

Mode estimation is a classical problem in statistics with a wide range of applications in machine learning. Despite this, there is little understanding in its robustness properties under possibly adversarial data contamination. In this paper, we give precise robustness guarantees as well as privacy guarantees under simple randomization. We then introduce a theory for multi-armed bandits where the values are the modes of the reward distributions instead of the mean. We prove regret guarantees for the problems of top arm identification, top m-arms identification, contextual modal bandits, and infinite continuous arms top arm recovery. We show in simulations that our algorithms are robust to perturbation of the arms by adversarial noise sequences, thus rendering modal bandits an attractive choice in situations where the rewards may have outliers or adversarial corruptions.

cs.LG↗

arXiv2020

Learning to Score Behaviors for Guided Policy Optimization

We introduce a new approach for comparing reinforcement learning policies, using Wasserstein distances (WDs) in a newly defined latent behavioral space. We show that by utilizing the dual formulation of the WD, we can learn score functions over policy behaviors that can in turn be used to lead policy optimization towards (or away from) (un)desired behaviors. Combined with smoothed WDs, the dual formulation allows us to devise efficient algorithms that take stochastic gradient descent steps through WD regularizers. We incorporate these regularizers into two novel on-policy algorithms, Behavior-Guided Policy Gradient and Behavior-Guided Evolution Strategies, which we demonstrate can outperform existing methods in a variety of challenging environments. We also provide an open source demo.

cs.LG↗

arXiv2020

Convergence Rates of Smooth Message Passing with Rounding in Entropy-Regularized MAP Inference

Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely configuration of the discrete-valued model. Linear programming (LP) relaxations in the Sherali-Adams hierarchy are widely used to attempt to solve this problem, and smooth message passing algorithms have been proposed to solve regularized versions of these LPs with great success. This paper leverages recent work in entropy-regularized LPs to analyze convergence rates of a class of edge-based smooth message passing algorithms to $ε$-optimality in the relaxation. With an appropriately chosen regularization constant, we present a theoretical guarantee on the number of iterations sufficient to recover the true integral MAP solution when the LP is tight and the solution is unique.

cs.LG↗

arXiv2020

Ready Policy One: World Building Through Active Learning

Model-Based Reinforcement Learning (MBRL) offers a promising direction for sample efficient learning, often achieving state of the art results for continuous control tasks. However, many existing MBRL methods rely on combining greedy policies with exploration heuristics, and even those which utilize principled exploration bonuses construct dual objectives in an ad hoc fashion. In this paper we introduce Ready Policy One (RP1), a framework that views MBRL as an active learning problem, where we aim to improve the world model in the fewest samples possible. RP1 achieves this by utilizing a hybrid objective function, which crucially adapts during optimization, allowing the algorithm to trade off reward v.s. exploration at different stages of learning. In addition, we introduce a principled mechanism to terminate sample collection once we have a rich enough trajectory batch to improve the model. We rigorously evaluate our method on a variety of continuous control tasks, and demonstrate statistically significant gains over existing approaches.

cs.LG↗

arXiv2020

Gen-Oja: A Two-time-scale approach for Streaming CCA

In this paper, we study the problems of principal Generalized Eigenvector computation and Canonical Correlation Analysis in the stochastic setting. We propose a simple and efficient algorithm, Gen-Oja, for these problems. We prove the global convergence of our algorithm, borrowing ideas from the theory of fast-mixing Markov chains and two-time-scale stochastic approximation, showing that it achieves the optimal rate of convergence. In the process, we develop tools for understanding stochastic processes with Markovian noise which might be of independent interest.

cs.LG↗

arXiv2019

Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning

We describe an application of Wasserstein distance to Reinforcement Learning. The Wasserstein distance in question is between the distribution of mappings of trajectories of a policy into some metric space, and some other fixed distribution (which may, for example, come from another policy). Different policies induce different distributions, so given an underlying metric, the Wasserstein distance quantifies how different policies are. This can be used to learn multiple polices which are different in terms of such Wasserstein distances by using a Wasserstein regulariser. Changing the sign of the regularisation parameter, one can learn a policy for which its trajectory mapping distribution is attracted to a given fixed distribution.

cs.LG↗

arXiv2019

Wasserstein Fair Classification

We propose an approach to fair classification that enforces independence between the classifier outputs and sensitive information by minimizing Wasserstein-1 distances. The approach has desirable theoretical properties and is robust to specific choices of the threshold used to obtain class predictions from model outputs. We introduce different methods that enable hiding sensitive information at test time or have a simple and fast implementation. We show empirical performance against different fairness baselines on several benchmark fairness datasets.

stat.ML↗

arXiv2019

Provably Robust Blackbox Optimization for Reinforcement Learning

Interest in derivative-free optimization (DFO) and "evolutionary strategies" (ES) has recently surged in the Reinforcement Learning (RL) community, with growing evidence that they can match state of the art methods for policy optimization problems in Robotics. However, it is well known that DFO methods suffer from prohibitively high sampling complexity. They can also be very sensitive to noisy rewards and stochastic dynamics. In this paper, we propose a new class of algorithms, called Robust Blackbox Optimization (RBO). Remarkably, even if up to $23\%$ of all the measurements are arbitrarily corrupted, RBO can provably recover gradients to high accuracy. RBO relies on learning gradient flows using robust regression methods to enable off-policy updates. On several MuJoCo robot control tasks, when all other RL approaches collapse in the presence of adversarial noise, RBO is able to train policies effectively. We also show that RBO can be applied to legged locomotion tasks including path tracking for quadruped robots.

cs.LG↗

arXiv2019

From Complexity to Simplicity: Adaptive ES-Active Subspaces for Blackbox Optimization

We present a new algorithm ASEBO for optimizing high-dimensional blackbox functions. ASEBO adapts to the geometry of the function and learns optimal sets of sensing directions, which are used to probe it, on-the-fly. It addresses the exploration-exploitation trade-off of blackbox optimization with expensive blackbox queries by continuously learning the bias of the lower-dimensional model used to approximate gradients of smoothings of the function via compressed sensing and contextual bandits methods. To obtain this model, it leverages techniques from the emerging theory of active subspaces in the novel ES blackbox optimization context. As a result, ASEBO learns the dynamically changing intrinsic dimensionality of the gradient space and adapts to the hardness of different stages of the optimization without external supervision. Consequently, it leads to more sample-efficient blackbox optimization than state-of-the-art algorithms. We provide theoretical results and test ASEBO advantages over other methods empirically by evaluating it on the set of reinforcement learning policy optimization tasks as well as functions from the recently open-sourced Nevergrad library.

math.OC↗

arXiv2019

Structured Monte Carlo Sampling for Nonisotropic Distributions via Determinantal Point Processes

We propose a new class of structured methods for Monte Carlo (MC) sampling, called DPPMC, designed for high-dimensional nonisotropic distributions where samples are correlated to reduce the variance of the estimator via determinantal point processes. We successfully apply DPPMCs to problems involving nonisotropic distributions arising in guided evolution strategy (GES) methods for RL, CMA-ES techniques and trust region algorithms for blackbox optimization, improving state-of-the-art in all these settings. In particular, we show that DPPMCs drastically improve exploration profiles of the existing evolution strategy algorithms. We further confirm our results, analyzing random feature map estimators for Gaussian mixture kernels. We provide theoretical justification of our empirical results, showing a connection between DPPMCs and structured orthogonal MC methods for isotropic distributions.

cs.LG↗

arXiv2018

Online learning with kernel losses

We present a generalization of the adversarial linear bandits framework, where the underlying losses are kernel functions (with an associated reproducing kernel Hilbert space) rather than linear functions. We study a version of the exponential weights algorithm and bound its regret in this setting. Under conditions on the eigendecay of the kernel we provide a sharp characterization of the regret for this algorithm. When we have polynomial eigendecay $μ_j \le \mathcal{O}(j^{-β})$, we find that the regret is bounded by $\mathcal{R}_n \le \mathcal{O}(n^{β/(2(β-1))})$; while under the assumption of exponential eigendecay $μ_j \le \mathcal{O}(e^{-βj })$, we get an even tighter bound on the regret $\mathcal{R}_n \le \mathcal{O}(n^{1/2}\log(n)^{1/2})$. We also study the full information setting when the underlying losses are kernel functions and present an adapted exponential weights algorithm and a conditional gradient descent algorithm.

stat.ML↗

arXiv2015

Real time clustering of time series using triangular potentials

Motivated by the problem of computing investment portfolio weightings we investigate various methods of clustering as alternatives to traditional mean-variance approaches. Such methods can have significant benefits from a practical point of view since they remove the need to invert a sample covariance matrix, which can suffer from estimation error and will almost certainly be non-stationary. The general idea is to find groups of assets which share similar return characteristics over time and treat each group as a single composite asset. We then apply inverse volatility weightings to these new composite assets. In the course of our investigation we devise a method of clustering based on triangular potentials and we present associated theoretical results as well as various examples based on synthetic data.

cs.LG↗

arXiv2011

Computational approaches to Poisson traces associated to finite subgroups of Sp(2n,C)

We reduce the computation of Poisson traces on quotients of symplectic vector spaces by finite subgroups of symplectic automorphisms to a finite one, by proving several results which bound the degrees of such traces as well as the dimension in each degree. This applies more generally to traces on all polynomial functions which are invariant under invariant Hamiltonian flow. We implement these approaches by computer together with direct computation for infinite families of groups, focusing on complex reflection and abelian subgroups of GL(2,C) < Sp(4,C), Coxeter groups of rank <= 3 and A_4, B_4=C_4, and D_4, and subgroups of SL(2,C).

math.SG↗