In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
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Question: Routing models, a form of conditional computation where examples are routed through a subset of components in a larger network, have shown promising results in recent works. Surprisingly, routing models to date have lacked important properties, such as architectural diversity and large numbers of routing decisions. Both architectural diversity and routing depth can increase the representational power of a routing network. In this work, we address both of these deficiencies. We discuss the significance of architectural diversity in routing models, and explain the tradeoffs between capacity and optimization when increasing routing depth. In our experiments, we find that adding architectural diversity to routing models significantly improves performance, cutting the error rates of a strong baseline by 35% on an Omniglot setup. However, when scaling up routing depth, we find that modern routing techniques struggle with optimization. We conclude by discussing both the positive and negative results, and suggest directions for future research.

Answer: Per-example routing models benefit from architectural diversity, but still struggle to scale to a large number of routing decisions.


Question: Careful tuning of the learning rate, or even schedules thereof, can be crucial to effective neural net training. There has been much recent interest in gradient-based meta-optimization, where one tunes hyperparameters, or even learns an optimizer, in order to minimize the expected loss when the training procedure is unrolled. But because the training procedure must be unrolled thousands of times, the meta-objective must be defined with an orders-of-magnitude shorter time horizon than is typical for neural net training. We show that such short-horizon meta-objectives cause a serious bias towards small step sizes, an effect we term short-horizon bias. We introduce a toy problem, a noisy quadratic cost function, on which we analyze short-horizon bias by deriving and comparing the optimal schedules for short and long time horizons. We then run meta-optimization experiments (both offline and online) on standard benchmark datasets, showing that meta-optimization chooses too small a learning rate by multiple orders of magnitude, even when run with a moderately long time horizon (100 steps) typical of work in the area. We believe short-horizon bias is a fundamental problem that needs to be addressed if meta-optimization is to scale to practical neural net training regimes.

Answer: We investigate the bias in the short-horizon meta-optimization objective.


Question: We consider tackling a single-agent RL problem by distributing it to $n$ learners. These learners, called advisors, endeavour to solve the problem from a different focus. Their advice, taking the form of action values, is then communicated to an aggregator, which is in control of the system. We show that the local planning method for the advisors is critical and that none of the ones found in the literature is flawless: the \textit{egocentric} planning overestimates values of states where the other advisors disagree, and the \textit{agnostic} planning is inefficient around danger zones. We introduce a novel approach called \textit{empathic} and discuss its theoretical aspects. We empirically examine and validate our theoretical findings on a fruit collection task.

Answer:
We consider tackling a single-agent RL problem by distributing it to $n$ learners.