Many real-world systems can be naturally described by mathematical formulas. The task of automatically constructing formulas to fit observed data is called symbolic regression. Evolutionary methods such as genetic programming have been commonly used to solve symbolic regression tasks, but they have significant drawbacks, such as high computational complexity. Recently, neural networks have been applied to symbolic regression, among which the transformer-based methods seem to be most promising. After training a transformer on a large number of formulas, the actual inference, i.e., finding a formula for new, unseen data, is very fast (in the order of seconds). This is considerably faster than state-of-the-art evolutionary methods. The main drawback of transformers is that they generate formulas without numerical constants, which have to be optimized separately, yielding suboptimal results. We propose a transformer-based approach called SymFormer, which predicts the formula by outputting the symbols and the constants simultaneously. This helps to generate formulas that fit the data more accurately. In addition, the constants provided by SymFormer serve as a good starting point for subsequent tuning via gradient descent to further improve the model accuracy. We show on several benchmarks that SymFormer outperforms state-of-the-art methods while having faster inference.

Visual navigation is essential for many applications in robotics, from manipulation, through mobile robotics to automated driving. Deep reinforcement learning (DRL) provides an elegant map-free approach integrating image processing, localization, and planning in one module, which can be trained and therefore optimized for a given environment. However, to date, DRL-based visual navigation was validated exclusively in simulation, where the simulator provides information that is not available in the real world, e.g., the robot's position or segmentation masks. This precludes the use of the learned policy on a real robot. Therefore, we present a novel approach that enables a direct deployment of the trained policy on real robots. We have designed a new powerful simulator capable of domain randomization. To facilitate the training, we propose visual auxiliary tasks and a tailored reward scheme. The policy is fine-tuned on images collected from real-world environments. We have evaluated the method on a mobile robot in a real office environment. The training took approximately 30 hours on a single GPU. In 30 navigation experiments, the robot reached a 0.3-meter neighbourhood of the goal in more than 86.7% of cases. This result makes the proposed method directly applicable to tasks like mobile manipulation.