相关论文: Monotone Conditional Complexity Bounds on Future P…
We study the worst-case complexity of a non-monotone line search framework that covers a wide variety of known techniques published in the literature. In this framework, the non-monotonicity is controlled by a sequence of nonnegative…
Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one…
Prediction via deterministic continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we build…
Forecasting accuracy is bounded by the information available about the future. This paper makes that statement precise using information-theoretic tools. Under logarithmic loss, the expected performance of any probabilistic forecast…
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…
Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as…
In this paper, we first prove a high probability bound rather than an expectation bound for stochastic optimization with smooth loss. Furthermore, the existing analysis requires the knowledge of optimal classifier for tuning the step size…
Solomonoff's central result on induction is that the posterior of a universal semimeasure M converges rapidly and with probability 1 to the true sequence generating posterior mu, if the latter is computable. Hence, M is eligible as a…
A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…
Recently, Arjevani et al. [1] established a lower bound of iteration complexity for the first-order optimization under an $L$-smooth condition and a bounded noise variance assumption. However, a thorough review of existing literature on…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional $canonical\ transformations$. Our findings contribute to establishing new global well-posedness results for…
The forecasting problem for a stationary and ergodic binary time series $\{X_n\}_{n=0}^{\infty}$ is to estimate the probability that $X_{n+1}=1$ based on the observations $X_i$, $0\le i\le n$ without prior knowledge of the distribution of…
One important goal of black-box complexity theory is the development of complexity models allowing to derive meaningful lower bounds for whole classes of randomized search heuristics. Complementing classical runtime analysis, black-box…
Many machine learning approaches are characterized by information constraints on how they interact with the training data. These include memory and sequential access constraints (e.g. fast first-order methods to solve stochastic…
We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However,…
We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) S when the measures are indexed by another poset A. We give counterexamples…
Monotone systems, also known as order-preserving or cooperative systems, are prevalent in models of engineering applications such as transportation and biological networks. In this paper, we investigate the problem of finding a control…
Let $\{X_n\}$ be a stationary and ergodic time series taking values from a finite or countably infinite set ${\cal X}$. Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times $\lambda_n$…
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…