Daily TMLR digest for Aug 02, 2022

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Aug 1, 2022, 8:00:12 PM8/1/22
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Accepted papers
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Title: Max-Affine Spline Insights Into Deep Network Pruning

Authors: Haoran You, Randall Balestriero, Zhihan Lu, Yutong Kou, Huihong Shi, Shunyao Zhang, Shang Wu, Yingyan Lin, Richard Baraniuk

Abstract: State-of-the-art (SOTA) approaches to deep network (DN) training overparametrize the model and then prune a posteriori to obtain a ``winning ticket'' subnetwork that can achieve high accuracy. Using a recently developed spline interpretation of DNs, we obtain novel insights into how DN pruning affects its mapping. In particular, under the realm of spline operators, we are able to pinpoint the impact of pruning onto the DN's underlying input space partition and per-region affine mappings, opening new avenues in understanding why and when are pruned DNs able to maintain high performance. We also discover that a DN's spline mapping exhibits an early-bird (EB) phenomenon whereby the spline's partition converges at early training stages, bridging the recently developed DN spline theory and lottery ticket hypothesis of DNs. We finally leverage this new insight to develop a principled and efficient pruning strategy whose goal is to prune isolated groups of nodes that have a redundant contribution in the forming of the spline partition.
Extensive experiments on four networks and three datasets validate that our new spline-based DN pruning approach reduces training FLOPs by up to 3.5x while achieving similar or even better accuracy than current state-of-the-art methods. Code is available at https://github.com/RICE-EIC/Spline-EB.

URL: https://openreview.net/forum?id=bMar2OkxVu

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Title: Did I do that? Blame as a means to identify controlled effects in reinforcement learning

Authors: Oriol Corcoll, Youssef Sherif Mansour Mohamed, Raul Vicente

Abstract: Affordance learning is a crucial ability of intelligent agents. This ability relies on understanding the different ways the environment can be controlled. Approaches encouraging RL agents to model controllable aspects of their environment have repeatedly achieved state-of-the-art results. Despite their success, these approaches have only been studied using generic tasks as a proxy but have not yet been evaluated in isolation. In this work, we study the problem of identifying controlled effects from a causal perspective. Humans compare counterfactual outcomes to assign a degree of blame to their actions. Following this idea, we propose Controlled Effect Network (CEN), a self-supervised method based on the causal concept of blame. CEN is evaluated in a wide range of environments against two state-of-the-art models, showing that it precisely identifies controlled effects.

URL: https://openreview.net/forum?id=NL2L3XjVFx

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New submissions
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Title: Approximate Policy Iteration with Bisimulation Metrics

Abstract: Bisimulation metrics define a distance measure between states of a Markov decision process (MDP) based on a comparison of reward sequences. Due to this property they provide theoretical guarantees in value function approximation (VFA). In this work we first prove that bisimulation and $\pi$-bisimulation metrics can be defined via a more general class of Sinkhorn distances, which unifies various state similarity metrics used in recent work. Then we describe an approximate policy iteration (API) procedure that uses a bisimulation-based discretization of the state space for VFA and prove asymptotic performance bounds. Next, we bound the difference between $\pi$-bisimulation metrics in terms of the change in the policies themselves. Based on these results, we design an API($\alpha$) procedure that employs conservative policy updates and enjoys better performance bounds than the naive API approach. We discuss how such API procedures map onto practical actor-critic methods that use bisimulation metrics for state representation learning. Lastly, we validate our theoretical results and investigate their practical implications via a controlled empirical analysis based on an implementation of bisimulation-based API for finite MDPs.

URL: https://openreview.net/forum?id=Ii7UeHc0mO

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Title: Local Kernel Ridge Regression for Scalable, Interpolating, Continuous Regression

Abstract: We study a localized version of kernel ridge regression that can continuously, smoothly interpolate the underlying function values which are highly non-linear with observed data points. This new method can deal with the data of which (a) local density is highly uneven and (b) the function values change dramatically in certain small but unknown regions. By introducing a new rank-based interpolation scheme, the interpolated values provided by our local method continuously vary with query points. Our method is scalable by avoiding the full matrix inverse, compared with traditional kernel ridge regression.

URL: https://openreview.net/forum?id=EDAk6F8yMM

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