Related papers: Agnostic Online Learning and Excellent Sets
The problem of piecewise affine (PWA) regression and planning is of foundational importance to the study of online learning, control, and robotics, where it provides a theoretically and empirically tractable setting to study systems…
We initiate a systematic investigation of the abstract elementary classes that have amalgamation, satisfy tameness (a locality property for orbital types), and are stable (in terms of the number of orbital types) in some cardinal. Assuming…
The goal of a learner in standard online learning is to maintain an average loss close to the loss of the best-performing single function in some class. In many real-world problems, such as rating or ranking items, there is no single best…
We study a variant of the Student-Project Allocation problem with lecturer preferences over Students where ties are allowed in the preference lists of students and lecturers (SPA-ST). We investigate the concept of strong stability in this…
A method for compression of large graphs and non-negative matrices to a block structure is proposed. Szemer\'edi's regularity lemma is used as heuristic motivation of the significance of stochastic block models. Another ingredient of the…
In this paper the existence and unicity of a stable periodic orbit is proven, for a class of piecewise affine differential equations in dimension 3 or more, provided their interaction structure is a negative feedback loop. It is also shown…
Maintaining predictive accuracy in non-stationary environments requires online model selection to adapt autonomously to unknown distribution shifts. However, existing tuning-free algorithms face a fundamental trade-off between robustness…
In this dissertation we study statistical and online learning problems from an optimization viewpoint.The dissertation is divided into two parts : I. We first consider the question of learnability for statistical learning problems in the…
Active learning seeks to build the best possible model with a budget of labelled data by sequentially selecting the next point to label. However the training set is no longer \textit{iid}, violating the conditions required by existing…
In the problem of online learning for changing environments, data are sequentially received one after another over time, and their distribution assumptions may vary frequently. Although existing methods demonstrate the effectiveness of…
Rabern recently proved that any graph with omega >= (3/4)(Delta+1) contains a stable set meeting all maximum cliques. We strengthen this result, proving that such a stable set exists for any graph with omega > (2/3)(Delta+1). This is tight,…
We study fast rates of convergence in the setting of nonparametric online regression, namely where regret is defined with respect to an arbitrary function class which has bounded complexity. Our contributions are two-fold: - In the…
We study the problem of online non-stochastic control (ONC), which is the control of a linear system under adversarial disturbances and adversarial cost functions, with the aim of minimizing the total cost incurred. A recent line of…
We study various discrete nonlinear combinatorial optimization problems in an online learning framework. In the first part, we address the question of whether there are negative results showing that getting a vanishing (or even vanishing…
Breaking of equivalence between the microcanonical ensemble and the canonical ensemble, describing a large system subject to hard and soft constraints, respectively, was recently shown to occur in large random graphs. Hard constraints must…
We prove analogues for hypergraphs of Szemer\'edi's regularity lemma and the associated counting lemma for graphs. As an application, we give the first combinatorial proof of the multidimensional Szemer\'edi theorem of Furstenberg and…
We investigate the complexity of approximately counting stable matchings in the $k$-attribute model, where the preference lists are determined by dot products of "preference vectors" with "attribute vectors", or by Euclidean distances…
We consider the problem of online prediction in a marginally stable linear dynamical system subject to bounded adversarial or (non-isotropic) stochastic perturbations. This poses two challenges. Firstly, the system is in general…
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop…
We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate…