A large body of animation research focuses on optimization of movement control, either as action sequences or policy parameters. However, as closed-form expressions of the objective functions are often not available, our understanding of the optimization problems is limited. Building on recent work on analyzing neural network training, we contribute novel visualizations of high-dimensional control optimization landscapes; this yields insights into why control optimization is hard and why common practices like early termination and spline-based action parameterizations make optimization easier. For example, our experiments show how trajectory optimization can become increasingly ill-conditioned with longer trajectories, but parameterizing control as partial target states—e.g., target angles converted to torques using a PD-controller—can act as an efficient preconditioner. Both our visualizations and quantitative empirical data also indicate that neural network policy optimization scales better than trajectory optimization for long planning horizons. Our work advances the understanding of movement optimization and our visualizations should also provide value in educational use.

中文翻译：

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可视化运动控制优化景观

大量动画研究侧重于运动控制的优化，无论是作为动作序列还是策略参数。然而，由于目标函数的封闭式表达式通常不可用，我们对优化问题的理解是有限的。基于最近分析神经网络训练的工作，我们贡献了高维控制优化景观的新颖可视化；这可以深入了解为什么控制优化很难，以及为什么像提前终止和基于样条的动作参数化这样的常见做法会使优化更容易。例如，我们的实验展示了轨迹优化如何随着更长的轨迹变得越来越病态，但是将控制参数化为部分目标状态——例如，使用 PD 控制器将目标角度转换为扭矩——可以作为有效的预调节器。我们的可视化和定量经验数据都表明，神经网络策略优化比轨迹优化更适合长期规划。我们的工作促进了对运动优化的理解，我们的可视化也应该在教育用途中提供价值。