Related papers: Comments on the Du-Kakade-Wang-Yang Lower Bounds
In reinforcement learning (RL) theory, the concept of most confusing instances is central to establishing regret lower bounds, that is, the minimal exploration needed to solve a problem. Given a reference model and its optimal policy, a…
Knowledge compilation studies the trade-off between succinctness and efficiency of different representation languages. For many languages, there are known strong lower bounds on the representation size, but recent work shows that, for some…
With regard to the recently published article, ``Y.-Q. Wang, et al., Physical mechanism of equiprobable exclusion network with heterogeneous interactions in phase transitions: Analytical analyses of steady state evolving from initial state,…
Convergence bounds are one of the main tools to obtain information on the performance of a distributed machine learning task, before running the task itself. In this work, we perform a set of experiments to assess to which extent, and in…
This paper offers a new perspective on the limits of machine learning: the ceiling on progress is set not by model size or algorithm choice but by the information structure of the task itself. Code generation has progressed more reliably…
Recently, self-supervised contrastive learning has achieved great success on various tasks. However, its underlying working mechanism is yet unclear. In this paper, we first provide the tightest bounds based on the widely adopted assumption…
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…
We derive sublinear regret bounds for undiscounted reinforcement learning in continuous state space. The proposed algorithm combines state aggregation with the use of upper confidence bounds for implementing optimism in the face of…
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…
We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average…
We revisit the range sampling problem: the input is a set of points where each point is associated with a real-valued weight. The goal is to store them in a structure such that given a query range and an integer $k$, we can extract $k$…
The replicability crisis has drawn attention to numerous weaknesses in psychology and social science research practice. In this work we focus on three issues that cannot be addressed with replication alone, and which deserve more attention:…
Involutive non-degenerate set theoretic solutions of the Yang-Baxter equation are considered, with a focus on finite solutions. A rich class of indecomposable and irretractable solutions is determined and necessary and sufficient conditions…
We propose a rigorous decomposition of predictive error, highlighting that not all 'irreducible' error is genuinely immutable. Many domains stand to benefit from iterative enhancements in measurement, construct validity, and modeling. Our…
Machine learning algorithms generally suffer from a problem of explainability. Given a classification result from a model, it is typically hard to determine what caused the decision to be made, and to give an informative explanation. We…
The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration…
The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is…
We propose a new PAC-Bayesian bound and a way of constructing a hypothesis space, so that the bound is convex in the posterior distribution and also convex in a trade-off parameter between empirical performance of the posterior distribution…
For any truncated path algebra $\Lambda$ of a quiver, we classify, by way of representation-theoretic invariants, the irreducible components of the parametrizing varieties $\mathbf{Rep}_{\mathbf{d}}(\Lambda)$ of the $\Lambda$-modules with…
This is a brief technical note to clarify the state of lower bounds on regret for reinforcement learning. In particular, this paper: - Reproduces a lower bound on regret for reinforcement learning, similar to the result of Theorem 5 in the…