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This work studies discrete-time discounted Markov decision processes with continuous state and action spaces and addresses the inverse problem of inferring a cost function from observed optimal behavior. We first consider the case in which…
We consider the problem of distribution-free learning for Boolean function classes in the PAC and agnostic models. Generalizing a beautiful work of Malach and Shalev-Shwartz (2022) that gave tight correlational SQ (CSQ) lower bounds for…
In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems. Given measurement variables and parameters, the Buckingham Pi theorem provides a procedure…
Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify…
We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off…
Learning problems in the text processing domain often map the text to a space whose dimensions are the measured features of the text, e.g., its words. Three characteristic properties of this domain are (a) very high dimensionality, (b) both…
We focus on a stochastic learning model where the learner observes a finite set of training examples and the output of the learning process is a data-dependent distribution over a space of hypotheses. The learned data-dependent distribution…
We investigate the teaching of infinite concept classes through the effect of the learning bias (which is used by the learner to prefer some concepts over others and by the teacher to devise the teaching examples) and the sampling bias…
Combining learned policies in a prioritized, ordered manner is desirable because it allows for modular design and facilitates data reuse through knowledge transfer. In control theory, prioritized composition is realized by null-space…
The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence. In an influential paper, Valiant recognised that the challenge of learning should be…
Margin-based learning, exemplified by linear and kernel methods, is one of the few classical settings where generalization guarantees are independent of the number of parameters. This makes it a central case study in modern highly…
Juedes and Lutz (1995) proved a small span theorem for polynomial-time many-one reductions in exponential time. This result says that for language A decidable in exponential time, either the class of languages reducible to A (the lower…
We introduce an information-theoretic framework that views learning as universal prediction under log loss, characterized through regret bounds. Central to the framework is an effective notion of architecture-based model complexity, defined…
Blumer et al. (1987, 1989) showed that any concept class that is learnable by Occam algorithms is PAC learnable. Board and Pitt (1990) showed a partial converse of this theorem: for concept classes that are closed under exception lists, any…
Online learning is a familiar problem setting within Machine-Learning in which data is presented serially in time to a learning agent, requiring it to progressively adapt within the constraints of the learning algorithm. More sophisticated…
Learning is a process wherein a learning agent enhances its performance through exposure of experience or data. Throughout this journey, the agent may encounter diverse learning environments. For example, data may be presented to the leaner…
Pursuing realistic results according to human visual perception is the central concern in the image transformation tasks. Perceptual learning approaches like perceptual loss are empirically powerful for such tasks but they usually rely on…
We give tight bounds on the relation between the primal and dual of various combinatorial dimensions, such as the pseudo-dimension and fat-shattering dimension, for multi-valued function classes. These dimensional notions play an important…
Deep neural networks have achieved remarkable success, yet our understanding of how they learn remains limited. These models can learn high-dimensional tasks, which is generally statistically intractable due to the curse of dimensionality.…
In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the…