Related papers: Comments on the Du-Kakade-Wang-Yang Lower Bounds
Restricted Lie algebras of dimension up to $3$ over algebraically closed fields of positive characteristic were classified by Wang and his collaborators in [25, 19]. In this paper, we obtain a classification of restricted Lie algebras of…
We consider the classification problem for finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak{osp}}_{2n|2m}$ with $n\geqslant 2$. We give necessary conditions for an…
A lower bound on the number of uncorrectable errors of weight half the minimum distance is derived for binary linear codes satisfying some condition. The condition is satisfied by some primitive BCH codes, extended primitive BCH codes,…
Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
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The Lambek calculus is a well-known logical formalism for modelling natural language syntax. The original calculus covered a substantial number of intricate natural language phenomena, but only those restricted to the context-free setting.…
As learning difficulty is crucial for machine learning (e.g., difficulty-based weighting learning strategies), previous literature has proposed a number of learning difficulty measures. However, no comprehensive investigation for learning…
Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior…
Poor sample efficiency is a major limitation of deep reinforcement learning in many domains. This work presents an attention-based method to project neural network inputs into an efficient representation space that is invariant under…
Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
Query evaluation on probabilistic databases is generally intractable (#P-hard). Existing dichotomy results have identified which queries are tractable (or safe), and connected them to tractable lineages. In our previous work, using…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
The DUCK-calculus presented here is a recent approach to cope with probabilistic uncertainty in a sound and efficient way. Uncertain rules with bounds for probabilities and explicit conditional independences can be maintained incrementally.…
Can simple algorithms with a good representation solve challenging reinforcement learning problems? In this work, we answer this question in the affirmative, where we take "simple learning algorithm" to be tabular Q-Learning, the "good…
Local versions of measurability have been around for a long time. Roughly, one splits the notion of $\mu $-completeness into pieces, and asks for a uniform ultrafilter over $\mu $ satisfying just some piece of $\mu $-completeness. Analogue…
Reinforcement learning is hard in general. Yet, in many specific environments, learning is easy. What makes learning easy in one environment, but difficult in another? We address this question by proposing a simple measure of…
There have been many recent advances on provably efficient Reinforcement Learning (RL) in problems with rich observation spaces. However, all these works share a strong realizability assumption about the optimal value function of the true…