To obtain better value estimation in reinforcement learning, we propose a novel algorithm based on the double actor-critic framework with temporal difference error-driven regularization, abbreviated as TDDR. TDDR employs double actors, with each actor paired with a critic, thereby fully leveraging the advantages of double critics. Additionally, TDDR introduces an innovative critic regularization architecture. Compared to classical deterministic policy gradient-based algorithms that lack a double actor-critic structure, TDDR provides superior estimation. Moreover, unlike existing algorithms with double actor-critic frameworks, TDDR does not introduce any additional hyperparameters, significantly simplifying the design and implementation process. The convergence of the proposed TDDR to the optimal value is analyzed under random updating and simultaneous updating patterns. Extensive experiments on various tasks, including MuJoCo and Box2D, demonstrate that TDDR performs competitively against 13 algorithms, including both benchmarks and state-of-the-art methods. It also achieves statistically significant performance gains across several environments.

Immersive virtual- and augmented-reality headsets can overlay a flat image against any surface or hang virtual objects in the space around the user. The technology is rapidly improving and may, in the long term, replace traditional flat panel displays in many situations. When displays are no longer intrinsically flat, how should we use the space around the user for abstract data visualisation? In this paper, we ask this question with respect to origin-destination flow data in a global geographic context. We report on the findings of three studies exploring different spatial encodings for flow maps. The first experiment focuses on different 2D and 3D encodings for flows on flat maps. We find that participants are significantly more accurate with raised flow paths whose height is proportional to flow distance but fastest with traditional straight line 2D flows. In our second and third experiment we compared flat maps, 3D globes and a novel interactive design we call MapsLink, involving a pair of linked flat maps. We find that participants took significantly more time with MapsLink than other flow maps while the 3D globe with raised flows was the fastest, most accurate, and most preferred method. Our work suggests that careful use of the third spatial dimension can resolve visual clutter in complex flow maps.

Abstract This paper explores different ways to render world‐wide geographic maps in virtual reality (VR). We compare: (a) a 3D exocentric globe, where the user's viewpoint is outside the globe; (b) a flat map (rendered to a plane in VR); (c) an egocentric 3D globe, with the viewpoint inside the globe; and (d) a curved map, created by projecting the map onto a section of a sphere which curves around the user. In all four visualisations the geographic centre can be smoothly adjusted with a standard handheld VR controller and the user, through a head‐tracked headset, can physically move around the visualisation. For distance comparison exocentric globe is more accurate than egocentric globe and flat map. For area comparison more time is required with exocentric and egocentric globes than with flat and curved maps. For direction estimation, the exocentric globe is more accurate and faster than the other visual presentations. Our study participants had a weak preference for the exocentric globe. Generally the curved map had benefits over the flat map. In almost all cases the egocentric globe was found to be the least effective visualisation. Overall, our results provide support for the use of exocentric globes for geographic visualisation in mixed‐reality.