Writing a mathematical paper is both an act of recording mathematical content and a means of communication of one's work. In contrast with other types of writing, the style of math papers is incredibly rigid and resistant to even modest innovation. As a result, both goals suffer, sometimes immeasurably. The clarity suffers the most, which…
One of the most popular posts on the Thesis Whisperer is How to write 1000 words a day and not go bat shit crazy. Last year a Twitter follower brought to my attention a post called How I went from writing 2000 words to 10,000 words a day by the fiction writer Rachel Aaron. I…
The Score Function Estimator Is Widely Used For Estimating Gradients Of Stochastic Objectives In Stochastic Computation Graphs (scg), Eg. In Reinforcement Learning And Meta-learning. While Deriving The First-order Gradient Estimators By Differentiating A Surrogate Loss (sl) Objective Is Computationally And Conceptually Simple, Using The Same Approach For Higher-order Gradients Is More Challenging. Firstly, Analytically Deriving And Implementing Such Estimators Is Laborious And Not Compliant With Automatic Differentiation. Secondly, Repeatedly Applying Sl To Construct New Objectives For Each Order Gradient Involves Increasingly Cumbersome Graph Manipulations. Lastly, To Match The First-order Gradient Under Differentiation, Sl Treats Part Of The Cost As A Fixed Sample, Which We Show Leads To Missing And Wrong Terms For Higher-order Gradient Estimators. To Address All These Shortcomings In A Unified Way, We Introduce Dice, Which Provides A Single Objective That Can Be Differentiated Repeatedly, Generating Correct Gradient Estimators Of Any Order In Scgs. Unlike Sl, Dice Relies On Automatic Differentiation For Performing The Requisite Graph Manipulations. We Verify The Correctness Of Dice Both Through A Proof And Through Numerical Evaluation Of The Dice Gradient Estimates. We Also Use Dice To Propose And Evaluate A Novel Approach For Multi-agent Learning. Our Code Is Available At Https://goo.gl/xkkgxn.
A Key Challenge In Complex Visuomotor Control Is Learning Abstract Representations That Are Effective For Specifying Goals, Planning, And Generalization. To This End, We Introduce Universal Planning Networks (upn). Upns Embed Differentiable Planning Within A Goal-directed Policy. This Planning Computation Unrolls A Forward Model In A Latent Space And Infers An Optimal Action Plan Through Gradient Descent Trajectory Optimization. The Plan-by-gradient-descent Process And Its Underlying Representations Are Learned End-to-end To Directly Optimize A Supervised Imitation Learning Objective. We Find That The Representations Learned Are Not Only Effective For Goal-directed Visual Imitation Via Gradient-based Trajectory Optimization, But Can Also Provide A Metric For Specifying Goals Using Images. The Learned Representations Can Be Leveraged To Specify Distance-based Rewards To Reach New Target States For Model-free Reinforcement Learning, Resulting In Substantially More Effective Learning When Solving New Tasks Described Via Image-based Goals. We Were Able To Achieve Successful Transfer Of Visuomotor Planning Strategies Across Robots With Significantly Different Morphologies And Actuation Capabilities.