Motivated by the connection between sampling and optimization, we study a mirror descent analogue of Langevin dynamics and analyze three different discretization schemes, giving nonasymptotic convergence rate under functional inequalities such as Log-Sobolev in the corresponding metric. Compared to the Euclidean setting, the result reveals intricate relationship between the underlying geometry and the target distribution and suggests that care might need to be taken in order for the discretized algorithm to achieve vanishing bias with diminishing stepsize for sampling from potentials under weaker smoothness/convexity regularity conditions.

Estimating the per-state expected cumulative rewards is a critical aspect of reinforcement learning approaches, however the experience is obtained, but standard deep neural-network function-approximation methods are often inefficient in this setting. An alternative approach, exemplified by value iteration networks, is to learn transition and reward models of a latent Markov decision process whose value predictions fit the data. This approach has been shown empirically to converge faster to a more robust solution in many cases, but there has been little theoretical study of this phenomenon. In this paper, we explore such implicit representations of value functions via theory and focused experimentation. We prove that, for a linear parametrization, gradient descent converges to global optima despite nonlinearity and non-convexity introduced by the implicit representation. Furthermore, we derive convergence rates for both cases which allow us to identify conditions under which stochastic gradient descent (SGD) with this implicit representation converges substantially faster than its explicit counterpart. Finally, we provide empirical results in some simple domains that illustrate the theoretical findings.

Estimating the per-state expected cumulative rewards is a critical aspect of reinforcement learning approaches, however the experience is obtained, but standard deep neural-network function-approximation methods are often inefficient in this setting. An alternative approach, exemplified by value iteration networks, is to learn transition and reward models of a latent Markov decision process whose value predictions fit the data. This approach has been shown empirically to converge faster to a more robust solution in many cases, but there has been little theoretical study of this phenomenon. In this paper, we explore such implicit representations of value functions via theory and focused experimentation. We prove that, for a linear parametrization, gradient descent converges to global optima despite nonlinearity and non-convexity introduced by the implicit representation. Furthermore, we derive convergence rates for both cases which allow us to identify conditions under which stochastic gradient descent (SGD) with this implicit representation converges substantially faster than its explicit counterpart. Finally, we provide empirical results in some simple domains that illustrate the theoretical findings.

Plus: DeepSeek has unveiled its long-awaited new AI model. When ChatGPT was released in late 2022, it showed how easily generative AI could create human-like text. This quickly caught the eye of cybercriminals, who began using LLMs to compose malicious emails. Since then, they've adopted AI for everything from turbocharged phishing and hyperrealistic deepfakes to automated vulnerability scans. Many organizations are now struggling to cope with the sheer volume of cyberattacks. AI is making them faster, cheaper, and easier to carry out, a problem set to worsen as more cybercriminals adopt these tools--and their capabilities improve.

This paper describes the OCCGEN toolkit, which allows extracting multilingual parallel data balanced in gender within occupations. OCCGEN can extract datasets that reflect gender diversity (beyond binary) more fairly in society to be further used to explicitly mitigate occupational gender stereotypes. We propose two use cases that extract evaluation datasets for machine translation in four high-resource languages from different linguistic families and in a low-resource African language. Our analysis of these use cases shows that translation outputs in high-resource languages tend to worsen in feminine subsets (compared to masculine), specially in the directions containing English. This is confirmed by the human evaluation. We hypothesize that a sound language generation may contribute to pay less attention to the source sentence and to overgeneralize to the most frequent gender forms.