Related papers: Fat Shattering, Joint Measurability, and PAC Learn…
We provide an exact non-asymptotic lower bound on the minimax expected excess risk (EER) in the agnostic probably-ap\-proximately-correct (PAC) machine learning classification model and identify minimax learning algorithms as certain…
The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature…
We study the problem of learning robust classifiers where the classifier will receive a perturbed input. Unlike robust PAC learning studied in prior work, here the clean data and its label are also adversarially chosen. We formulate this…
Recently, there has been remarkable progress in reinforcement learning (RL) with general function approximation. However, all these works only provide regret or sample complexity guarantees. It is still an open question if one can achieve…
Partial observability is a common challenge in many reinforcement learning applications, which requires an agent to maintain memory, infer latent states, and integrate this past information into exploration. This challenge leads to a number…
Many prominent quantum computing algorithms with applications in fields such as chemistry and materials science require a large number of measurements, which represents an important roadblock for future real-world use cases. We introduce a…
Exchangeable random variables form an important and well-studied generalization of i.i.d. variables, however simple examples show that no nontrivial concept or function classes are PAC learnable under general exchangeable data inputs…
Sample complexity bounds are a common performance metric in the Reinforcement Learning literature. In the discounted cost, infinite horizon setting, all of the known bounds have a factor that is a polynomial in $1/(1-\gamma)$, where $\gamma…
Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an…
We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate…
Generalized quantum measurements (also known as POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform…
The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…
This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method…
Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework. More specifically we consider the following task: Given samples from some unknown…
We propose a learning model called the quantum statistical learning QSQ model, which extends the SQ learning model introduced by Kearns to the quantum setting. Our model can be also seen as a restriction of the quantum PAC learning model:…
We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective…
We study risk-sensitive reinforcement learning in finite discounted MDPs with recursive entropic risk measures (ERM), where the risk parameter $\beta \neq 0$ controls the agent's risk attitude: $\beta>0$ for risk-averse and $\beta<0$ for…
Similarly to quantum states, also quantum measurements can be "mixed", corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely…
We revisit the recently introduced Local Glivenko-Cantelli setting, which studies distribution-dependent uniform convergence rates of the Empirical Mean Estimator (EME). In this work, we investigate generalizations of this setting where…
There has been a recent interest in understanding and characterizing the sample complexity of list learning tasks, where the learning algorithm is allowed to make a short list of $k$ predictions, and we simply require one of the predictions…