arXiv subjects

Alejandro Ribeiro

Publications and source records attributed to Alejandro Ribeiro.

At least 217 records · Page 12Linked to original sources

arXiv2020

Efficient Distributed Hessian Free Algorithm for Large-scale Empirical Risk Minimization via Accumulating Sample Strategy

In this paper, we propose a Distributed Accumulated Newton Conjugate gradiEnt (DANCE) method in which sample size is gradually increasing to quickly obtain a solution whose empirical loss is under satisfactory statistical accuracy. Our proposed method is multistage in which the solution of a stage serves as a warm start for the next stage which contains more samples (including the samples in the previous stage). The proposed multistage algorithm reduces the number of passes over data to achieve the statistical accuracy of the full training set. Moreover, our algorithm in nature is easy to be distributed and shares the strong scaling property indicating that acceleration is always expected by using more computing nodes. Various iteration complexity results regarding descent direction computation, communication efficiency and stopping criteria are analyzed under convex setting. Our numerical results illustrate that the proposed method outperforms other comparable methods for solving learning problems including neural networks.

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arXiv2020

Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks

We consider the problem of optimally allocating resources across a set of transmitters and receivers in a wireless network. The resulting optimization problem takes the form of constrained statistical learning, in which solutions can be found in a model-free manner by parameterizing the resource allocation policy. Convolutional neural networks architectures are an attractive option for parameterization, as their dimensionality is small and does not scale with network size. We introduce the random edge graph neural network (REGNN), which performs convolutions over random graphs formed by the fading interference patterns in the wireless network. The REGNN-based allocation policies are shown to retain an important permutation equivariance property that makes them amenable to transference to different networks. We further present an unsupervised model-free primal-dual learning algorithm to train the weights of the REGNN. Through numerical simulations, we demonstrate the strong performance REGNNs obtain relative to heuristic benchmarks and their transference capabilities.

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arXiv2020

Graphon Pooling in Graph Neural Networks

Graph neural networks (GNNs) have been used effectively in different applications involving the processing of signals on irregular structures modeled by graphs. Relying on the use of shift-invariant graph filters, GNNs extend the operation of convolution to graphs. However, the operations of pooling and sampling are still not clearly defined and the approaches proposed in the literature either modify the graph structure in a way that does not preserve its spectral properties, or require defining a policy for selecting which nodes to keep. In this work, we propose a new strategy for pooling and sampling on GNNs using graphons which preserves the spectral properties of the graph. To do so, we consider the graph layers in a GNN as elements of a sequence of graphs that converge to a graphon. In this way we have no ambiguity in the node labeling when mapping signals from one layer to the other and a spectral representation that is consistent throughout the layers. We evaluate this strategy in a synthetic and a real-world numerical experiment where we show that graphon pooling GNNs are less prone to overfitting and improve upon other pooling techniques, especially when the dimensionality reduction ratios between layers is large.

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arXiv2020

Sufficiently Accurate Model Learning

Modeling how a robot interacts with the environment around it is an important prerequisite for designing control and planning algorithms. In fact, the performance of controllers and planners is highly dependent on the quality of the model. One popular approach is to learn data driven models in order to compensate for inaccurate physical measurements and to adapt to systems that evolve over time. In this paper, we investigate a method to regularize model learning techniques to provide better error characteristics for traditional control and planning algorithms. This work proposes learning "Sufficiently Accurate" models of dynamics using a primal-dual method that can explicitly enforce constraints on the error in pre-defined parts of the state-space. The result of this method is that the error characteristics of the learned model is more predictable and can be better utilized by planning and control algorithms. The characteristics of Sufficiently Accurate models are analyzed through experiments on a simulated ball paddle system.

cs.LG↗

arXiv2020

Approximate Supermodularity of Kalman Filter Sensor Selection

This work considers the problem of selecting sensors in a large scale system to minimize the error in estimating its states. More specifically, the state estimation mean-square error(MSE) and worst-case error for Kalman filtering and smoothing. Such selection problems are in general NP-hard, i.e., their solution can only be approximated in practice even for moderately large problems. Due to its low complexity and iterative nature, greedy algorithms are often used to obtain these approximations by selecting one sensor at a time choosing at each step the one that minimizes the estimation performance metric. When this metric is supermodular, this solution is guaranteed to be (1-1/e)-optimal. This is however not the case for the MSE or the worst-case error. This issue is often circumvented by using supermodular surrogates, such as the logdet, despite the fact that minimizing the logdet is not equivalent to minimizing the MSE. Here, this issue is addressed by leveraging the concept of approximate supermodularity to derive near-optimality certificates for greedily minimizing the estimation mean-square and worst-case error. In typical application scenarios, these certificates approach the (1-1/e) guarantee obtained for supermodular functions, thus demonstrating that no change to the original problem is needed to obtain guaranteed good performance.

math.OC↗

arXiv2020

Wireless Power Control via Counterfactual Optimization of Graph Neural Networks

We consider the problem of downlink power control in wireless networks, consisting of multiple transmitter-receiver pairs communicating with each other over a single shared wireless medium. To mitigate the interference among concurrent transmissions, we leverage the network topology to create a graph neural network architecture, and we then use an unsupervised primal-dual counterfactual optimization approach to learn optimal power allocation decisions. We show how the counterfactual optimization technique allows us to guarantee a minimum rate constraint, which adapts to the network size, hence achieving the right balance between average and $5^{th}$ percentile user rates throughout a range of network configurations.

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arXiv2020

The empirical duality gap of constrained statistical learning

This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to incorporate prior knowledge and impose desired structural and statistical properties on the solutions. Still, solving constrained statistical problems remains challenging and guarantees scarce, leaving them to be tackled using regularized formulations. Though practical and effective, selecting regularization parameters so as to satisfy requirements is challenging, if at all possible, due to the lack of a straightforward relation between parameters and constraints. In this work, we propose to directly tackle the constrained statistical problem overcoming its infinite dimensionality, unknown distributions, and constraints by leveraging finite dimensional parameterizations, sample averages, and duality theory. Aside from making the problem tractable, these tools allow us to bound the empirical duality gap, i.e., the difference between our approximate tractable solutions and the actual solutions of the original statistical problem. We demonstrate the effectiveness and usefulness of this constrained formulation in a fair learning application.

cs.LG↗

arXiv2019

Risk-Aware MMSE Estimation

Despite the simplicity and intuitive interpretation of Minimum Mean Squared Error (MMSE) estimators, their effectiveness in certain scenarios is questionable. Indeed, minimizing squared errors on average does not provide any form of stability, as the volatility of the estimation error is left unconstrained. When this volatility is statistically significant, the difference between the average and realized performance of the MMSE estimator can be drastically different. To address this issue, we introduce a new risk-aware MMSE formulation which trades between mean performance and risk by explicitly constraining the expected predictive variance of the involved squared error. We show that, under mild moment boundedness conditions, the corresponding risk-aware optimal solution can be evaluated explicitly, and has the form of an appropriately biased nonlinear MMSE estimator. We further illustrate the effectiveness of our approach via several numerical examples, which also showcase the advantages of risk-aware MMSE estimation against risk-neutral MMSE estimation, especially in models involving skewed, heavy-tailed distributions.

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arXiv2019

Graph Policy Gradients for Large Scale Robot Control

In this paper, we consider the problem of learning policies to control a large number of homogeneous robots. To this end, we propose a new algorithm we call Graph Policy Gradients (GPG) that exploits the underlying graph symmetry among the robots. The curse of dimensionality one encounters when working with a large number of robots is mitigated by employing a graph convolutional neural (GCN) network to parametrize policies for the robots. The GCN reduces the dimensionality of the problem by learning filters that aggregate information among robots locally, similar to how a convolutional neural network is able to learn local features in an image. Through experiments on formation flying, we show that our proposed method is able to scale better than existing reinforcement methods that employ fully connected networks. More importantly, we show that by using our locally learned filters we are able to zero-shot transfer policies trained on just three robots to over hundred robots.

cs.RO↗

arXiv2019

Rethinking Sketching as Sampling: A Graph Signal Processing Approach

Sampling of signals belonging to a low-dimensional subspace has well-documented merits for dimensionality reduction, limited memory storage, and online processing of streaming network data. When the subspace is known, these signals can be modeled as bandlimited graph signals. Most existing sampling methods are designed to minimize the error incurred when reconstructing the original signal from its samples. Oftentimes these parsimonious signals serve as inputs to computationally-intensive linear operators. Hence, interest shifts from reconstructing the signal itself towards approximating the output of the prescribed linear operator efficiently. In this context, we propose a novel sampling scheme that leverages graph signal processing, exploiting the low-dimensional (bandlimited) structure of the input as well as the transformation whose output we wish to approximate. We formulate problems to jointly optimize sample selection and a sketch of the target linear transformation, so when the latter is applied to the sampled input signal the result is close to the desired output. Similar sketching as sampling ideas are also shown effective in the context of linear inverse problems. Because these designs are carried out off line, the resulting sampling plus reduced-complexity processing pipeline is particularly useful for data that are acquired or processed in a sequential fashion, where the linear operator has to be applied fast and repeatedly to successive inputs or response signals. Numerical tests showing the effectiveness of the proposed algorithms include classification of handwritten digits from as few as 20 out of 784 pixels in the input images and selection of sensors from a network deployed to carry out a distributed parameter estimation task.

cs.IT↗

arXiv2019

A Prediction-Correction Algorithm for Real-Time Model Predictive Control

In this work we adapt a prediction-correction algorithm for continuous time-varying convex optimization problems to solve dynamic programs arising from Model Predictive Control. In particular, the prediction step tracks the evolution of the optimal solution of the problem which depends on the current state of the system. The cost of said step is that of inverting one Hessian and it guarantees, under some conditions, that the iterate remains in the quadratic convergence region of the optimization problem at the next time step. These conditions imply (i) that the variation of the state in a control interval cannot be too large and that (ii) the solution computed in the previous time step needs to be sufficiently accurate. The latter can be guaranteed by running classic Newton iterations, which we term correction steps. Since this method exhibits quadratic convergence the number of iterations to achieve a desired accuracy $η$ is of order $\log_2\log_2 1/η$, where the cost of each iteration is approximately that of inverting a Hessian. This grants the prediction-correction control law low computational complexity. In addition, the solution achieved by the algorithm is such that the closed loop system remains stable, which allows extending the applicability of Model Predictive Control to systems with faster dynamics and less computational power. Numerical examples where we consider nonlinear systems support the theoretical conclusions.

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arXiv2019

Model-Free Learning of Optimal Ergodic Policies in Wireless Systems

Learning optimal resource allocation policies in wireless systems can be effectively achieved by formulating finite dimensional constrained programs which depend on system configuration, as well as the adopted learning parameterization. The interest here is in cases where system models are unavailable, prompting methods that probe the wireless system with candidate policies, and then use observed performance to determine better policies. This generic procedure is difficult because of the need to cull accurate gradient estimates out of these limited system queries. This paper constructs and exploits smoothed surrogates of constrained ergodic resource allocation problems, the gradients of the former being representable exactly as averages of finite differences that can be obtained through limited system probing. Leveraging this unique property, we develop a new model-free primal-dual algorithm for learning optimal ergodic resource allocations, while we rigorously analyze the relationships between original policy search problems and their surrogates, in both primal and dual domains. First, we show that both primal and dual domain surrogates are uniformly consistent approximations of their corresponding original finite dimensional counterparts. Upon further assuming the use of near-universal policy parameterizations, we also develop explicit bounds on the gap between optimal values of initial, infinite dimensional resource allocation problems, and dual values of their parameterized smoothed surrogates. In fact, we show that this duality gap decreases at a linear rate relative to smoothing and universality parameters. Thus, it can be made arbitrarily small at will, also justifying our proposed primal-dual algorithmic recipe. Numerical simulations confirm the effectiveness of our approach.

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arXiv2019

The Graphon Fourier Transform

In many network problems, graphs may change by the addition of nodes, or the same problem may need to be solved in multiple similar graphs. This generates inefficiency, as analyses and systems that are not transferable have to be redesigned. To address this, we consider graphons, which are both limit objects of convergent graph sequences and random graph models. We define graphon signals and introduce the Graphon Fourier Transform (WFT), to which the Graph Fourier Transform (GFT) is shown to converge. This result is demonstrated in two numerical experiments where, as expected, the GFT converges, hinting to the possibility of centralizing analysis and design on graphons to leverage transferability.

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arXiv2019

Invariance-Preserving Localized Activation Functions for Graph Neural Networks

Graph signals are signals with an irregular structure that can be described by a graph. Graph neural networks (GNNs) are information processing architectures tailored to these graph signals and made of stacked layers that compose graph convolutional filters with nonlinear activation functions. Graph convolutions endow GNNs with invariance to permutations of the graph nodes' labels. In this paper, we consider the design of trainable nonlinear activation functions that take into consideration the structure of the graph. This is accomplished by using graph median filters and graph max filters, which mimic linear graph convolutions and are shown to retain the permutation invariance of GNNs. We also discuss modifications to the backpropagation algorithm necessary to train local activation functions. The advantages of localized activation function architectures are demonstrated in four numerical experiments: source localization on synthetic graphs, authorship attribution of 19th century novels, movie recommender systems and scientific article classification. In all cases, localized activation functions are shown to improve model capacity.

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arXiv2019

Control-Aware Scheduling for Low Latency Wireless Systems with Deep Learning

We consider the problem of scheduling transmissions over low-latency wireless communication links to control various control systems. Low-latency requirements are critical in developing wireless technology for industrial control and Tactile Internet, but are inherently challenging to meet while also maintaining reliable performance. An alternative to ultra reliable low latency communications is a framework in which reliability is adapted to control system demands. We formulate the control-aware scheduling problem as a constrained statistical optimization problem in which the optimal scheduler is a function of current control and channel states. The scheduler is parameterized with a deep neural network, and the constrained problem is solved using techniques from primal-dual learning, which have a necessary model-free property in that they do not require explicit knowledge of channels models, performance metrics, or system dynamics to execute. The resulting control-aware deep scheduler is evaluated in empirical simulations and strong performance is shown relative to other model-free heuristic scheduling methods.

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arXiv2019

Scheduling Low Latency Traffic for Wireless Control Systems in 5G Networks

We consider the problem of allocating 5G radio resources over wireless communication links to control a series of independent low-latency wireless control systems common in industrial settings. Each control system sends state information to the base station to compute control signals under tight latency requirements. Such latency requirements can be met by restricting the uplink traffic to a single subframe in each 5G frame, thus ensuring a millisecond latency bound while leaving the remaining subframes available for scheduling overhead and coexisting broadband traffic. A linear assignment problem can be formulated to minimize the expected number of packet drops, but this alone is not sufficient to achieve good performance. We propose an optimal scheduling with respect to a control operation cost that allocates resources based on current control system needs. The resulting control-aware scheduling method is tested in simulation experiments that show drastically improved performance in 5G settings relative to control-agnostic scheduling under the proposed time-sliced frame structure.

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arXiv2019

Constrained Reinforcement Learning Has Zero Duality Gap

Autonomous agents must often deal with conflicting requirements, such as completing tasks using the least amount of time/energy, learning multiple tasks, or dealing with multiple opponents. In the context of reinforcement learning~(RL), these problems are addressed by (i)~designing a reward function that simultaneously describes all requirements or (ii)~combining modular value functions that encode them individually. Though effective, these methods have critical downsides. Designing good reward functions that balance different objectives is challenging, especially as the number of objectives grows. Moreover, implicit interference between goals may lead to performance plateaus as they compete for resources, particularly when training on-policy. Similarly, selecting parameters to combine value functions is at least as hard as designing an all-encompassing reward, given that the effect of their values on the overall policy is not straightforward. The later is generally addressed by formulating the conflicting requirements as a constrained RL problem and solved using Primal-Dual methods. These algorithms are in general not guaranteed to converge to the optimal solution since the problem is not convex. This work provides theoretical support to these approaches by establishing that despite its non-convexity, this problem has zero duality gap, i.e., it can be solved exactly in the dual domain, where it becomes convex. Finally, we show this result basically holds if the policy is described by a good parametrization~(e.g., neural networks) and we connect this result with primal-dual algorithms present in the literature and we establish the convergence to the optimal solution.

cs.LG↗

arXiv2019

Optimal Resource Allocation in Wireless Control Systems via Deep Policy Gradient

In wireless control systems, remote control of plants is achieved through closing of the control loop over a wireless channel. As wireless communication is noisy and subject to packet dropouts, proper allocation of limited resources, e.g. transmission power, across plants is critical for maintaining reliable operation. In this paper, we formulate the design of an optimal resource allocation policy that uses current plant states and wireless channel states to assign resources used to send control actuation information back to plants. While this problem is challenging due to its infinite dimensionality and need for explicit system model and state knowledge, we propose the use of deep reinforcement learning techniques to find neural network-based resource allocation policies. In particular, we use model-free policy gradient methods to directly learn continuous power allocation policies without knowledge of plant dynamics or communication models. Numerical simulations demonstrate the strong performance of learned policies relative to baseline resource allocation methods in settings where state information is available both with and without noise.

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