We investigate approaches to regularisation during fine-tuning of deep neural networks. First we provide a neural network generalisation bound based on Rademacher complexity that uses the distance the weights have moved from their initial values. This bound has no direct dependence on the number of weights and compares favourably to other bounds when applied to convolutional networks. Our bound is highly relevant for fine-tuning, because providing a network with a good initialisation based on transfer learning means that learning can modify the weights less, and hence achieve tighter generalisation. Inspired by this, we develop a simple yet effective fine-tuning algorithm that constrains the hypothesis class to a small sphere centred on the initial pre-trained weights, thus obtaining provably better generalisation performance than conventional transfer learning. Empirical evaluation shows that our algorithm works well, corroborating our theoretical results. It outperforms both state of the art fine-tuning competitors, and penalty-based alternatives that we show do not directly constrain the radius of the search space.

In this paper, we provide a unified convergence analysis for a class of shuffling-type gradient methods for solving a well-known finite-sum minimization problem commonly used in machine learning. This algorithm covers various variants such as randomized reshuffling, single shuffling, and cyclic/incremental gradient schemes. We consider two different settings: strongly convex and non-convex problems. Our main contribution consists of new non-asymptotic and asymptotic convergence rates for a general class of shuffling-type gradient methods to solve both non-convex and strongly convex problems. While our rate in the non-convex problem is new (i.e. not known yet under standard assumptions), the rate on the strongly convex case matches (up to a constant) the best-known results. However, unlike existing works in this direction, we only use standard assumptions such as smoothness and strong convexity. Finally, we empirically illustrate the effect of learning rates via a non-convex logistic regression and neural network examples.

Policy optimization methods are one of the most widely used classes of Reinforcement Learning (RL) algorithms. Yet, so far, such methods have been mostly analyzed from an optimization perspective, without addressing the problem of exploration, or by making strong assumptions on the interaction with the environment. In this paper we consider model-based RL in the tabular finite-horizon MDP setting with unknown transitions and bandit feedback. For this setting, we propose an optimistic trust region policy optimization (TRPO) algorithm for which we establish $\tilde O(\sqrt{S^2 A H^4 K})$ regret for stochastic rewards. Furthermore, we prove $\tilde O( \sqrt{ S^2 A H^4 } K^{2/3} ) $ regret for adversarial rewards. Interestingly, this result matches previous bounds derived for the bandit feedback case, yet with known transitions. To the best of our knowledge, the two results are the first sub-linear regret bounds obtained for policy optimization algorithms with unknown transitions and bandit feedback.

Unmanned aerial vehicle (UAV) swarms must exploit machine learning (ML) in order to execute various tasks ranging from coordinated trajectory planning to cooperative target recognition. However, due to the lack of continuous connections between the UAV swarm and ground base stations (BSs), using centralized ML will be challenging, particularly when dealing with a large volume of data. In this paper, a novel framework is proposed to implement distributed federated learning (FL) algorithms within a UAV swarm that consists of a leading UAV and several following UAVs. Each following UAV trains a local FL model based on its collected data and then sends this trained local model to the leading UAV who will aggregate the received models, generate a global FL model, and transmit it to followers over the intra-swarm network. To identify how wireless factors, like fading, transmission delay, and UAV antenna angle deviations resulting from wind and mechanical vibrations, impact the performance of FL, a rigorous convergence analysis for FL is performed. Then, a joint power allocation and scheduling design is proposed to optimize the convergence rate of FL while taking into account the energy consumption during convergence and the delay requirement imposed by the swarm's control system. Simulation results validate the effectiveness of the FL convergence analysis and show that the joint design strategy can reduce the number of communication rounds needed for convergence by as much as 35% compared with the baseline design.

In continual learning, the learner faces a stream of data whose distribution changes over time. Modern neural networks are known to suffer under this setting, as they quickly forget previously acquired knowledge. To address such catastrophic forgetting, many continual learning methods implement different types of experience replay, re-learning on past data stored in a small buffer known as episodic memory. In this work, we complement experience replay with a new objective that we call anchoring, where the learner uses bilevel optimization to update its knowledge on the current task, while keeping intact the predictions on some anchor points of past tasks. These anchor points are learned using gradient-based optimization to maximize forgetting, which is approximated by fine-tuning the currently trained model on the episodic memory of past tasks. Experiments on several supervised learning benchmarks for continual learning demonstrate that our approach improves the standard experience replay in terms of both accuracy and forgetting metrics and for various sizes of episodic memories.

Many applications of artificial intelligence, ranging from credit lending to the design of medical diagnosis support tools through recidivism prediction, involve scoring individuals using a learned function of their attributes. These predictive risk scores are used to rank a set of people, and/or take individual decisions about them based on whether the score exceeds a certain threshold that may depend on the context in which the decision is taken. The level of delegation granted to such systems will heavily depend on how questions of fairness can be answered. While this concern has received a lot of attention in the classification setup, the design of relevant fairness constraints for the problem of learning scoring functions has not been much investigated. In this paper, we propose a flexible approach to group fairness for the scoring problem with binary labeled data, a standard learning task referred to as bipartite ranking. We argue that the functional nature of the ROC curve, the gold standard measuring ranking performance in this context, leads to several possible ways of formulating fairness constraints. We introduce general classes of fairness conditions in bipartite ranking and establish generalization bounds for scoring rules learned under such constraints. Beyond the theoretical formulation and results, we design practical learning algorithms and illustrate our approach with numerical experiments.

Deep Learning based Automatic Speech Recognition (ASR) models are very successful, but hard to interpret. To gain better understanding of how Artificial Neural Networks (ANNs) accomplish their tasks, introspection methods have been proposed. Adapting such techniques from computer vision to speech recognition is not straight-forward, because speech data is more complex and less interpretable than image data. In this work, we introduce Gradient-adjusted Neuron Activation Profiles (GradNAPs) as means to interpret features and representations in Deep Neural Networks. GradNAPs are characteristic responses of ANNs to particular groups of inputs, which incorporate the relevance of neurons for prediction. We show how to utilize GradNAPs to gain insight about how data is processed in ANNs. This includes different ways of visualizing features and clustering of GradNAPs to compare embeddings of different groups of inputs in any layer of a given network. We demonstrate our proposed techniques using a fully-convolutional ASR model.

We performed a massive evaluation of neural networks with architectures corresponding to random graphs of various types. Apart from the classical random graph families including random, scale-free and small world graphs, we introduced a novel and flexible algorithm for directly generating random directed acyclic graphs (DAG) and studied a class of graphs derived from functional resting state fMRI networks. A majority of the best performing networks were indeed in these new families. We also proposed a general procedure for turning a graph into a DAG necessary for a feed-forward neural network. We investigated various structural and numerical properties of the graphs in relation to neural network test accuracy. Since none of the classical numerical graph invariants by itself seems to allow to single out the best networks, we introduced new numerical characteristics that selected a set of quasi-1-dimensional graphs, which were the majority among the best performing networks.

We consider the problem of learning in Linear Quadratic Control systems whose transition parameters are initially unknown. Recent results in this setting have demonstrated efficient learning algorithms with regret growing with the square root of the number of decision steps. We present new efficient algorithms that achieve, perhaps surprisingly, regret that scales only (poly)logarithmically with the number of steps in two scenarios: when only the state transition matrix $A$ is unknown, and when only the state-action transition matrix $B$ is unknown and the optimal policy satisfies a certain non-degeneracy condition. On the other hand, we give a lower bound that shows that when the latter condition is violated, square root regret is unavoidable.

Continuous deep learning architectures have recently re-emerged as variants of Neural Ordinary Differential Equations (Neural ODEs). The infinite-depth approach offered by these models theoretically bridges the gap between deep learning and dynamical systems; however, deciphering their inner working is still an open challenge and most of their applications are currently limited to the inclusion as generic black-box modules. In this work, we "open the box" and offer a system-theoretic perspective, including state augmentation strategies and robustness, with the aim of clarifying the influence of several design choices on the underlying dynamics. We also introduce novel architectures: among them, a Galerkin-inspired depth-varying parameter model and neural ODEs with data-controlled vector fields.