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Adding constraint support in Machine Learning has the potential to address outstanding issues in data-driven AI systems, such as safety and fairness. Existing approaches typically apply constrained optimization techniques to ML training,…
Policy gradient methods in reinforcement learning update policy parameters by taking steps in the direction of an estimated gradient of policy value. In this paper, we consider the statistically efficient estimation of policy gradients from…
Using methods of statistical mechanics, we analyse the effect of outliers on the supervised learning of a classification problem. The learning strategy aims at selecting informative examples and discarding outliers. We compare two…
In this work we define a unified mathematical framework to deepen our understanding of the role of stochastic gradient (SG) noise on the behavior of Markov chain Monte Carlo sampling (SGMCMC) algorithms. Our formulation unlocks the design…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the…
Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…
Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a…
Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability,…
Controller design faces a trade-off between robustness and performance, and the reliability of linear controllers has caused many practitioners to focus on the former. However, there is renewed interest in improving system performance to…
Stochastic model predictive control has been a successful and robust control framework for many robotics tasks where the system dynamics model is slightly inaccurate or in the presence of environment disturbances. Despite the successes, it…
We analyze the learning properties of the stochastic gradient method when multiple passes over the data and mini-batches are allowed. We study how regularization properties are controlled by the step-size, the number of passes and the…
Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which…
Machine learning is now ubiquitous in societal decision-making, for example in evaluating job candidates or loan applications, and it is increasingly important to take into account how classified agents will react to the learning…
In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…
Monotonicity constraints are powerful regularizers in statistical modelling. They can support fairness in computer-aided decision making and increase plausibility in data-driven scientific models. The seminal min-max (MM) neural network…
Support vector machines (SVM) is one of the well known supervised classes of learning algorithms. Furthermore, the conic-segmentation SVM (CS-SVM) is a natural multiclass analogue of the standard binary SVM, as CS-SVM models are dealing…
We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together…
This paper investigates methods for estimating the optimal stochastic control policy for a Markov Decision Process with unknown transition dynamics and an unknown reward function. This form of model-free reinforcement learning comprises…
State space models (SSMs) have gained attention by showing potential to outperform Transformers. However, previous studies have not sufficiently addressed the mechanisms underlying their high performance owing to a lack of theoretical…