This article provides a rigorous analysis of convergence and stability of Episodic Upside-Down Reinforcement Learning, Goal-Conditioned Supervised Learning and Online Decision Transformers. These algorithms performed competitively across various benchmarks, from games to robotic tasks, but their theoretical understanding is limited to specific environmental conditions. This work initiates a theoretical foundation for algorithms that build on the broad paradigm of approaching reinforcement learning through supervised learning or sequence modeling. At the core of this investigation lies the analysis of conditions on the underlying environment, under which the algorithms can identify optimal solutions. We also assess whether emerging solutions remain stable in situations where the environment is subject to tiny levels of noise. Specifically, we study the continuity and asymptotic convergence of command-conditioned policies, values and the goal-reaching objective depending on the transition kernel of the underlying Markov Decision Process. We demonstrate that near-optimal behavior is achieved if the transition kernel is located in a sufficiently small neighborhood of a deterministic kernel. The mentioned quantities are continuous (with respect to a specific topology) at deterministic kernels, both asymptotically and after a finite number of learning cycles. The developed methods allow us to present the first explicit estimates on the convergence and stability of policies and values in terms of the underlying transition kernels. On the theoretical side we introduce a number of new concepts to reinforcement learning, like working in segment spaces, studying continuity in quotient topologies and the application of the fixed-point theory of dynamical systems. The theoretical study is accompanied by a detailed investigation of example environments and numerical experiments.

Scientists have discovered a technique whereby light can be bent around corners, inspired by the way clouds scatter sunlight. This type of light-bending could lead to advances in medical imaging, electronics cooling and even nuclear reactor design. Daniele Faccio at the University of Glasgow, UK, and his colleagues say they are shocked this type of light scattering wasn't noticed before. It works on the same basis as clouds, snow and other white materials that absorb light: once photons hit the surface of such a material, they are scattered in all directions, barely penetrating at all and getting reflected out the way they came. For instance, when sunlight hits a tall cumulonimbus cloud, it bounces off the top, making this part of the cloud appear bright white.

Artificial intelligence (AI) can use a person's brainwaves to see around corners and create images of objects the human eye can not directly see. Researchers at the University of Glasgow have shown that the computational imaging technique, known as "ghost imaging", can be combined with human vision to reconstruct the image of objects hidden from view by analyzing how the brain processes barely visible reflections on a wall. Ghost imaging has been used before to reveal objects hidden around corners and normally involves beaming laser light onto a surface, around a corner and back to a camera sensor, then using algorithms to decode the scattered returned light to identify the object. For the new study, researchers swapped out the camera for human eyes. Although the researchers previously used human vision in a passive manner to perform ghost imaging, the new work uses the human visual system in an active role by having a person view the light patterns instead of a camera.

The future is here, and it is every bit as cool and creepy as you might have hoped. X-ray vision has always been pretty far down on my list of superpowers I'd like to possess, far behind time travel and reading minds. But x-ray vision might be closer to reality than the other options, and I'll take what I can get. Researchers at the University of Glasgow are working to combine artificial intelligence and human brainwaves to identify objects around the corner -- objects that humans can't normally see because it's around a corner. It's called a "ghost imaging" system and will be presented at the Optica Imaging and Applied Optics Congress this month.