In reinforcement learning (RL), it is common to apply techniques used broadly in machine learning such as neural network function approximators and momentum-based optimizers. However, such tools were largely developed for supervised learning rather than nonstationary RL, leading practitioners to adopt target networks, clipped policy updates, and other RL-specific implementation tricks to combat this mismatch, rather than directly adapting this toolchain for use in RL. In this paper, we take a different approach and instead address the effect of nonstationarity by adapting the widely used Adam optimiser. We first analyse the impact of nonstationary gradient magnitude --- such as that caused by a change in target network --- on Adam's update size, demonstrating that such a change can lead to large updates and hence sub-optimal performance.To address this, we introduce Adam-Rel.Rather than using the global timestep in the Adam update, Adam-Rel uses the local timestep within an epoch, essentially resetting Adam's timestep to 0 after target changes.We demonstrate that this avoids large updates and reduces to learning rate annealing in the absence of such increases in gradient magnitude. Evaluating Adam-Rel in both on-policy and off-policy RL, we demonstrate improved performance in both Atari and Craftax.We then show that increases in gradient norm occur in RL in practice, and examine the differences between our theoretical model and the observed data.

Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion process. This paper explores Rolling Diffusion: a new approach that uses a sliding window denoising process. It ensures that the diffusion process progressively corrupts through time by assigning more noise to frames that appear later in a sequence, reflecting greater uncertainty about the future as the generation process unfolds. Empirically, we show that when the temporal dynamics are complex, Rolling Diffusion is superior to standard diffusion. In particular, this result is demonstrated in a video prediction task using the Kinetics-600 video dataset and in a chaotic fluid dynamics forecasting experiment.

A Ukrainian military drone has damaged a building in central Moscow, causing an explosion that was heard across the city's business district in the latest attack on the Russian capital by unmanned aerial vehicles. Moscow Mayor Sergei Sobyanin said in a statement on the Telegram messaging app that air defence systems had shot down a drone early on Friday morning and debris had fallen on the city's Expo Center. The Expo Center – a large event space used for major exhibitions – is located less than 5km (3.1 miles) from the Kremlin. A video published by Russian media outlets showed thick smoke rising next to skyscrapers in the city. The Russian defence ministry said that Ukraine launched the drone attack at about 4am local time (01:00 GMT) "using an unmanned aerial vehicle against objects located in Moscow and the Moscow region".

Abstract: We study the existence and regularity of local times for general d-dimensional stochastic processes. We give a general condition for their existence and regularity properties. To emphasize the contribution of our results, we show that they include various prominent examples, among others solutions to stochastic differential equations driven by fractional Brownian motion, where the behavior of the local time was not fully understood up to now and remained as an open problem in the stochastic analysis literature. In particular this completes the picture regarding the local time behavior of such equations, above all includes high dimensions and both large and small Hurst parameters. As other main examples, we also show that by using our general approach, one can quite easily cover and extend some recently obtained results on the local times of the Rosenblatt process and Gaussian quasi-helices.

Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their practicability suffers from the assumption of known dynamics of the underlying stochastic process, raising the statistical challenge of developing purely data-driven strategies. For the mathematically separated classes of continuous diffusion processes and L\'evy processes, we show that developing efficient strategies for related singular stochastic control problems can essentially be reduced to finding rate-optimal estimators with respect to the sup-norm risk of objects associated to the invariant distribution of ergodic processes which determine the theoretical solution of the control problem. From a statistical perspective, we exploit the exponential $\beta$-mixing property as the common factor of both scenarios to drive the convergence analysis, indicating that relying on general stability properties of Markov processes is a sufficiently powerful and flexible approach to treat complex applications requiring statistical methods. We show moreover that in the L\'evy case $-$ even though per se jump processes are more difficult to handle both in statistics and control theory $-$ a fully data-driven strategy with regret of significantly better order than in the diffusion case can be constructed.

India's Polar Satellite Launch Vehicle (PSLV-C37) has launched into space 88 satellites from earth imaging company Planet Labs, giving the startup the ability to "image all of Earth's landmass every day." Planet Labs earlier this month entered into an agreement to acquire Google's Terra Bella business, including the SkySat constellation of satellites, and said that Google upon closing, will enter into a multi-year contract to purchase Earth-imaging data from Planet. The startup expects its data to be useful for a variety of applications such as measuring agricultural yields, monitoring natural resources, or aiding first responders after natural disasters. The launch of the PSLV-37 on Wednesday morning local time was a record for India's space program as it carried 104 satellites into orbit, the largest number so far on a single launch. Launched from the Satish Dhawan Space Centre at Sriharikota in south India, the PSLV-C37 launched its primary payload, the 714 kilograms Cartosat-2 series satellite for earth observation, and 103 co-passenger satellites that weighed about 663 kg at lift-off into a 505 kilometer polar Sun Synchronous Orbit.