We propose a trust region method for policy optimization that employs Quasi-Newton approximation for the Hessian, called Quasi-Newton Trust Region Policy Optimization QNTRPO. Gradient descent is the de facto algorithm for reinforcement learning tasks with continuous controls. The algorithm has achieved state-of-the-art performance when used in reinforcement learning across a wide range of tasks. However, the algorithm suffers from a number of drawbacks including: lack of stepsize selection criterion, and slow convergence. We investigate the use of a trust region method using dogleg step and a Quasi-Newton approximation for the Hessian for policy optimization. We demonstrate through numerical experiments over a wide range of challenging continuous control tasks that our particular choice is efficient in terms of number of samples and improves performance

Model-free reinforcement learning attempts to find an optimal control action for an unknown dynamical system by directly searching over the parameter space of controllers. The convergence behavior and statistical properties of these approaches are often poorly understood because of the nonconvex nature of the underlying optimization problems as well as the lack of exact gradient computation. In this paper, we take a step towards demystifying the performance and efficiency of such methods by focusing on the standard infinite-horizon linear quadratic regulator problem for continuous-time systems with unknown state-space parameters. We establish exponential stability for the ordinary differential equation (ODE) that governs the gradient-flow dynamics over the set of stabilizing feedback gains and show that a similar result holds for the gradient descent method that arises from the forward Euler discretization of the corresponding ODE. We also provide theoretical bounds on the convergence rate and sample complexity of a random search method. Our results demonstrate that the required simulation time for achieving $\epsilon$-accuracy in a model-free setup and the total number of function evaluations both scale as $\log \, (1/\epsilon)$.

In 2012, the return of the Porsche Factory Team to the top LMP1 class was officially announced. This is how the Porsche 919 Hybrid was born. In 2014 was the first season, when the 919 took part in the FIA World Endurance Championship racing series and Porsche managed to achieve the overall 3rd place in its first season. During the next 3 seasons 2015, 2016 and 2017 the Porsche 919 Hybrid dominated the racing series and managed to achieve the hattrick both in terms of victories in 24-hours of Le Mans as well as overall series victory. All summed up, the 6 Championship titles and 3 overall victories in Le Mans in 4 seasons made the Porsche 919 Hybrid a legend.

The classic Bribery problem is to find a minimal subset of voters who need to change their vote to make some preferred candidate win. Its important generalizations consider voters who are weighted and also have different prices. We provide an approximate solution for these problems for a broad family of scoring rules (which includes Borda, t-approval, and Dowdall), in the following sense: for constant weights and prices, if there exists a strategy which costs Ψ, we efficiently find a strategy which costs at most Ψ Õ( Ψ). An extension for non-constant weights and prices is also given. Our algorithm is based on a randomized reduction from these Bribery generalizations to weighted coalitional manipulation (WCM). To solve this WCM instance, we apply the Birkhoff-von Neumann (BvN) decomposition to a fractional manipulation matrix. This allows us to limit the size of the possible ballot search space reducing it from exponential to polynomial, while still obtaining good approximation guarantees. Finding a solution in the truncated search space yields a new algorithm for WCM, which is of independent interest.

Semi-supervised ordinal regression (S$^2$OR) problems are ubiquitous in real-world applications, where only a few ordered instances are labeled and massive instances remain unlabeled. Recent researches have shown that directly optimizing concordance index or AUC can impose a better ranking on the data than optimizing the traditional error rate in ordinal regression (OR) problems. In this paper, we propose an unbiased objective function for S$^2$OR AUC optimization based on ordinal binary decomposition approach. Besides, to handle the large-scale kernelized learning problems, we propose a scalable algorithm called QS$^3$ORAO using the doubly stochastic gradients (DSG) framework for functional optimization. Theoretically, we prove that our method can converge to the optimal solution at the rate of $O(1/t)$, where $t$ is the number of iterations for stochastic data sampling. Extensive experimental results on various benchmark and real-world datasets also demonstrate that our method is efficient and effective while retaining similar generalization performance.

--Operating envelope is an important concept in industrial operations. Accurate identification for operating envelope can be extremely beneficial to stakeholders as it provides a set of operational parameters that optimizes some key performance indicators (KPI) such as product quality, operational safety, equipment efficiency, environmental impact, etc. Given the importance, data-driven approaches for computing the operating envelope are gaining popularity. These approaches typically use classifiers such as support vector machines, to set the operating envelope by learning the boundary in the operational parameter spaces between the manually assigned'large KPI' and'small KPI' groups. One challenge to these approaches is that the assignment to these groups is often ad-hoc and hence arbitrary. However, a bigger challenge with these approaches is that they don't take into account two key features that are needed to operationalize operating envelopes: (i) interpretability of the envelope by the operator and (ii) implementability of the envelope from a practical standpoint. In this work, we propose a new definition for operating envelope which directly targets the expected magnitude of KPI (i.e., no need to arbitrarily bin the data instances into groups) and accounts for the interpretability and the implementability. We then propose a regularized'GA penalty' algorithm that outputs an envelope where the user can tradeoff between bias and variance. The validity of our proposed algorithm is demonstrated by two sets of simulation studies and an application to a real-world challenge in the mining processes of a flotation plant. In industrial operations, an important concept is that of the operating envelope. Conceptually, the operating envelope is a set of operational parameters, such that some KPI is optimized. In the industrial context, typical KPIs include product quality, operational safety, equipment efficiency, environmental impact, etc [1]-[4]. The operating envelope has wide application since it directly targets the business outcome and yields actionable recommendations in the operations space.

We view the Information Bottleneck Principle (IBP: Tishby et al., 1999; Schwartz-Ziv and Tishby, 2017) and Predictive Information Bottleneck Principle (PIBP: Still et al., 2007; Alemi, 2019) as special cases of a family of general information bottleneck objectives (IBOs). Each IBO corresponds to a particular constrained optimization problem where the constraints apply to: (a) the mutual information between the training data and the learned model parameters or extracted representation of the data, and (b) the mutual information between the learned model parameters or extracted representation of the data and the test data (if any). The heuristics behind the IBP and PIBP are shown to yield different constraints in the corresponding constrained optimization problem formulations. We show how other heuristics lead to a new IBO, different from both the IBP and PIBP, and use the techniques from (Alemi, 2019) to derive and optimize a variational upper bound on the new IBO. We then apply the theory of general IBOs to resolve the seeming contradiction between, on the one hand, the recommendations of IBP and PIBP to maximize the mutual information between the model parameters and test data, and on the other, recent information-theoretic results (see Xu and Raginsky, 2017) suggesting that this mutual information should be minimized. The key insight is that the heuristics (and thus the constraints in the constrained optimization problems) of IBP and PIBP are not applicable to the scenario analyzed by (Xu and Raginsky, 2017) because the latter makes the additional assumption that the parameters of the trained model have been selected to minimize the empirical loss function. Aided by this insight, we formulate a new IBO that accounts for this property of the parameters of the trained model, and derive and optimize a variational bound on this IBO.

In this paper, we try to uncover the second-order essence of several first-order optimization methods. For Nesterov Accelerated Gradient, we rigorously prove that the algorithm makes use of the difference between past and current gradients, thus approximates the Hessian and accelerates the training. For adaptive methods, we related Adam and Adagrad to a powerful technique in computation statistics---Natural Gradient Descent. These adaptive methods can in fact be treated as relaxations of NGD with only a slight difference lying in the square root of the denominator in the update rules. Skeptical about the effect of such difference, we design a new algorithm---AdaSqrt, which removes the square root in the denominator and scales the learning rate by sqrt(T). Surprisingly, our new algorithm is comparable to various first-order methods(such as SGD and Adam) on MNIST and even beats Adam on CIFAR-10! This phenomenon casts doubt on the convention view that the square root is crucial and training without it will lead to terrible performance. As far as we have concerned, so long as the algorithm tries to explore second or even higher information of the loss surface, then proper scaling of the learning rate alone will guarantee fast training and good generalization performance. To the best of our knowledge, this is the first paper that seriously considers the necessity of square root among all adaptive methods. We believe that our work can shed light on the importance of higher-order information and inspire the design of more powerful algorithms in the future.

We consider distributed online convex optimization problems, where the distributed system consists of various computing units connected through a time-varying communication graph. In each time step, each computing unit selects a constrained vector, experiences a loss equal to an arbitrary convex function evaluated at this vector, and may communicate to its neighbors in the graph. The objective is to minimize the system-wide loss accumulated over time. We propose a decentralized algorithm with regret and cumulative constraint violation in $\mathcal{O}(T^{\max\{c,1-c\} })$ and $\mathcal{O}(T^{1-c/2})$, respectively, for any $c\in (0,1)$, where $T$ is the time horizon. When the loss functions are strongly convex, we establish improved regret and constraint violation upper bounds in $\mathcal{O}(\log(T))$ and $\mathcal{O}(\sqrt{T\log(T)})$. These regret scalings match those obtained by state-of-the-art algorithms and fundamental limits in the corresponding centralized online optimization problem (for both convex and strongly convex loss functions). In the case of bandit feedback, the proposed algorithms achieve a regret and constraint violation in $\mathcal{O}(T^{\max\{c,1-c/3 \} })$ and $\mathcal{O}(T^{1-c/2})$ for any $c\in (0,1)$. We numerically illustrate the performance of our algorithms for the particular case of distributed online regularized linear regression problems.

We present Free-MESSAGEp, the first zeroth-order algorithm for convex mean-semideviation-based risk-aware learning, which is also the first three-level zeroth-order compositional stochastic optimization algorithm, whatsoever. Using a non-trivial extension of Nesterov's classical results on Gaussian smoothing, we develop the Free-MESSAGEp algorithm from first principles, and show that it essentially solves a smoothed surrogate to the original problem, the former being a uniform approximation of the latter, in a useful, convenient sense. We then present a complete analysis of the Free-MESSAGEp algorithm, which establishes convergence in a user-tunable neighborhood of the optimal solutions of the original problem, as well as explicit convergence rates for both convex and strongly convex costs. Orderwise, and for fixed problem parameters, our results demonstrate no sacrifice in convergence speed compared to existing first-order methods, while striking a certain balance among the condition of the problem, its dimensionality, as well as the accuracy of the obtained results, naturally extending previous results in zeroth-order risk-neutral learning.