The ability to learn and adapt in real time is a central feature of biological systems. Neuromorphic architectures demonstrating such versatility can greatly enhance our ability to efficiently process information at the edge. A key challenge, however, is to understand which learning rules are best suited for specific tasks and how the relevant hyperparameters can be fine-tuned. In this work, we introduce a conceptual framework in which the learning process is integrated into the network itself. This allows us to cast meta-learning as a mathematical optimization problem. We employ DeepHyper, a scalable, asynchronous model-based search, to simultaneously optimize the choice of meta-learning rules and their hyperparameters. We demonstrate our approach with two different datasets, MNIST and FashionMNIST, using a network architecture inspired by the learning center of the insect brain. Our results show that optimal learning rules can be dataset-dependent even within similar tasks. This dependency demonstrates the importance of introducing versatility and flexibility in the learning algorithms. It also illuminates experimental findings in insect neuroscience that have shown a heterogeneity of learning rules within the insect mushroom body.

Determining the optimal location of control cabinet components requires the exploration of a large configuration space. For real-world control cabinets it is impractical to evaluate all possible cabinet configurations. Therefore, we need to apply methods for intelligent exploration of cabinet configuration space that enable to find a near-optimal configuration without evaluation of all possible configurations. In this paper, we describe an approach for multi-objective optimization of control cabinet layout that is based on Pareto Simulated Annealing. Optimization aims at minimizing the total wire length used for interconnection of components and the heat convection within the cabinet. We simulate heat convection to study the warm air flow within the control cabinet and determine the optimal position of components that generate heat during the operation. We evaluate and demonstrate the effectiveness of our approach empirically for various control cabinet sizes and usage scenarios.

Many set selection and ranking algorithms have recently been enhanced with diversity constraints that aim to explicitly increase representation of historically disadvantaged populations, or to improve the overall representativeness of the selected set. An unintended consequence of these constraints, however, is reduced in-group fairness: the selected candidates from a given group may not be the best ones, and this unfairness may not be well-balanced across groups. In this paper we study this phenomenon using datasets that comprise multiple sensitive attributes. We then introduce additional constraints, aimed at balancing the \in-group fairness across groups, and formalize the induced optimization problems as integer linear programs. Using these programs, we conduct an experimental evaluation with real datasets, and quantify the feasible trade-offs between balance and overall performance in the presence of diversity constraints.

Data-driven model training is increasingly relying on finding Nash equilibria with provable techniques, e.g., for GANs and multi-agent RL. In this paper, we analyse a new extra-gradient method, that performs gradient extrapolations and updates on a random subset of players at each iteration. This approach provably exhibits the same rate of convergence as full extra-gradient in non-smooth convex games. We propose an additional variance reduction mechanism for this to hold for smooth convex games. Our approach makes extrapolation amenable to massive multiplayer settings, and brings empirical speed-ups, in particular when using cyclic sampling schemes. We demonstrate the efficiency of player sampling on large-scale non-smooth and non-strictly convex games. We show that the joint use of extrapolation and player sampling allows to train better GANs on CIFAR10.

Many signal processing algorithms break the target signal into overlapping segments (also called windows, or patches), process them separately, and then stitch them back into place to produce a unified output. At the overlaps, the final value of those samples that are estimated more than once needs to be decided in some way. Averaging, the simplest approach, tends to produce blurred results. Significant work has been devoted to this issue in recent years: several works explore the idea of a weighted average of the overlapped patches and/or pixels; a more recent approach is to promote agreement (consensus) between the patches at their intersections. This work investigates the case where consensus is imposed as a hard constraint on the restoration problem. This leads to a general framework applicable to all sorts of signals, problems, decomposition strategies, and featuring a number of theoretical and practical advantages over other similar methods. The framework itself consists of a general optimization problem and a simple and efficient \admm-based algorithm for solving it. We also show that the consensus step of the algorithm, which is the main bottleneck of similar methods, can be solved efficiently and easily for any arbitrary patch decomposition scheme. As an example of the potential of our framework, we propose a method for filling missing samples (inpainting) which can be applied to signals of any dimension, and show its effectiveness on audio, image and video signals.

Policy gradients methods are perhaps the most widely used class of reinforcement learning algorithms. These methods apply to complex, poorly understood, control problems by performing stochastic gradient descent over a parameterized class of polices. Unfortunately, even for simple control problems solvable by classical techniques, policy gradient algorithms face non-convex optimization problems and are widely understood to converge only to local minima. This work identifies structural properties -- shared by finite MDPs and several classic control problems -- which guarantee that policy gradient objective function has no suboptimal local minima despite being non-convex. When these assumptions are relaxed, our work gives conditions under which any local minimum is near-optimal, where the error bound depends on a notion of the expressive capacity of the policy class.

We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of $\ell_\infty$ regression, we achieves an $O(\epsilon^{-4/5})$ iteration complexity, breaking the $O(\epsilon^{-1})$ barrier so far present for previous methods. We arrive at a similar rate for the problem of $\ell_1$-SVM, going beyond what is attainable by first-order methods with prox-oracle access for non-smooth non-strongly convex problems. We further show how to achieve even faster rates by introducing higher-order regularization. Our results rely on recent advances in near-optimal accelerated methods for higher-order smooth convex optimization. In particular, we extend Nesterov's smoothing technique to show that the standard softmax approximation is not only smooth in the usual sense, but also \emph{higher-order} smooth. With this observation in hand, we provide the first example of higher-order acceleration techniques yielding faster rates for \emph{non-smooth} optimization, to the best of our knowledge.

Boosting variational inference (BVI) approximates an intractable probability density by iteratively building up a mixture of simple component distributions one at a time, using techniques from sparse convex optimization to provide both computational scalability and approximation error guarantees. But the guarantees have strong conditions that do not often hold in practice, resulting in degenerate component optimization problems; and we show that the ad-hoc regularization used to prevent degeneracy in practice can cause BVI to fail in unintuitive ways. We thus develop universal boosting variational inference (UBVI), a BVI scheme that exploits the simple geometry of probability densities under the Hellinger metric to prevent the degeneracy of other gradient-based BVI methods, avoid difficult joint optimizations of both component and weight, and simplify fully-corrective weight optimizations. We show that for any target density and any mixture component family, the output of UBVI converges to the best possible approximation in the mixture family, even when the mixture family is misspecified. We develop a scalable implementation based on exponential family mixture components and standard stochastic optimization techniques. Finally, we discuss statistical benefits of the Hellinger distance as a variational objective through bounds on posterior probability, moment, and importance sampling errors. Experiments on multiple datasets and models show that UBVI provides reliable, accurate posterior approximations.

We study online convex optimization in a setting where the learner seeks to minimize the sum of a per-round hitting cost and a movement cost which is incurred when changing decisions between rounds. We prove a new lower bound on the competitive ratio of any online algorithm in the setting where the costs are $m$-strongly convex and the movement costs are the squared $\ell_2$ norm. This lower bound shows that no algorithm can achieve a competitive ratio that is $o(m^{-1/2})$ as $m$ tends to zero. No existing algorithms have competitive ratios matching this bound, and we show that the state-of-the-art algorithm, Online Balanced Decent (OBD), has a competitive ratio that is $\Omega(m^{-2/3})$. We additionally propose two new algorithms, Greedy OBD (G-OBD) and Regularized OBD (R-OBD) and prove that both algorithms have an $O(m^{-1/2})$ competitive ratio. The result for G-OBD holds when the hitting costs are quasiconvex and the movement costs are the squared $\ell_2$ norm, while the result for R-OBD holds when the hitting costs are $m$-strongly convex and the movement costs are Bregman Divergences. Further, we show that R-OBD simultaneously achieves constant, dimension-free competitive ratio and sublinear regret when hitting costs are strongly convex.

We propose a new metaheuristic training scheme that combines Stochastic Gradient Descent (SGD) and Discrete Optimization in an unconventional way. Our idea is to define a discrete neighborhood of the current SGD point containing a number of "potentially good moves" that exploit gradient information, and to search this neighborhood by using a classical metaheuristic scheme borrowed from Discrete Optimization. In the present paper we investigate the use of a simple Simulated Annealing (SA) metaheuristic that accepts/rejects a candidate new solution in the neighborhood with a probability that depends both on the new solution quality and on a parameter (the temperature) which is modified over time to lower the probability of accepting worsening moves. We use this scheme as an automatic way to perform hyper-parameter tuning, hence the title of the paper. A distinctive feature of our scheme is that hyper-parameters are modified within a single SGD execution (and not in an external loop, as customary) and evaluated on the fly on the current minibatch, i.e., their tuning is fully embedded within the SGD algorithm. The use of SA for training is not new, but previous proposals were mainly intended for non-differentiable objective functions for which SGD is not applied due to the lack of gradients. On the contrary, our SA method requires differentiability of (a proxy of) the loss function, and leverages on the availability of a gradient direction to define local moves that have a large probability to improve the current solution. Computational results on image classification (CIFAR-10) are reported, showing that the proposed approach leads to an improvement of the final validation accuracy for modern Deep Neural Networks such as ResNet34 and VGG16.