Knowing the learning dynamics of policy is significant to unveiling the mysteries of Reinforcement Learning (RL). It is especially crucial yet challenging to Deep RL, from which the remedies to notorious issues like sample inefficiency and learning instability could be obtained. In this paper, we study how the policy networks of typical DRL agents evolve during the learning process by empirically investigating several kinds of temporal change for each policy parameter. In popular MuJoCo and DeepMind Control Suite (DMC) environments, we find common phenomena for TD3 and RAD agents: (1) the activity of policy network parameters is highly asymmetric and policy networks advance monotonically along a very limited number of major parameter directions; (2) severe detours occur in parameter update and harmonic-like changes are observed for all minor parameter directions. By performing a novel temporal SVD along the policy learning path, the major and minor parameter directions are identified as the columns of the right unitary matrix associated with dominant and insignificant singular values respectively. Driven by the discoveries above, we propose a simple and effective method, called Policy Path Trimming and Boosting (PPTB), as a general plug-in improvement to DRL algorithms. The key idea of PPTB is to trim the policy learning path by canceling the policy updates in minor parameter directions, and boost the learning path by encouraging the advance in major directions. In experiments, we demonstrate that our method improves the learning performance of TD3, RAD, and DoubleDQN regarding scores and efficiency in MuJoCo, DMC, and MinAtar tasks respectively.

Knowing the learning dynamics of policy is significant to unveiling the mysteries of Reinforcement Learning (RL). It is especially crucial yet challenging to Deep RL, from which the remedies to notorious issues like sample inefficiency and learning instability could be obtained. In this paper, we study how the policy networks of typical DRL agents evolve during the learning process by empirically investigating several kinds of temporal change for each policy parameter. In popular MuJoCo and DeepMind Control Suite (DMC) environments, we find common phenomena for TD3 and RAD agents: (1) the activity of policy network parameters is highly asymmetric and policy networks advance monotonically along a very limited number of major parameter directions; (2) severe detours occur in parameter update and harmonic-like changes are observed for all minor parameter directions. By performing a novel temporal SVD along the policy learning path, the major and minor parameter directions are identified as the columns of the right unitary matrix associated with dominant and insignificant singular values respectively.

Much of mechanistic interpretability has focused on understanding the activation spaces of large neural networks. However, activation space-based approaches reveal little about the underlying circuitry used to compute features. To better understand the circuits employed by models, we introduce a new decomposition method called Local Loss Landscape Decomposition (L3D). L3D identifies a set of low-rank subnetworks: directions in parameter space of which a subset can reconstruct the gradient of the loss between any sample's output and a reference output vector. We design a series of progressively more challenging toy models with well-defined subnetworks and show that L3D can nearly perfectly recover the associated subnetworks. Additionally, we investigate the extent to which perturbing the model in the direction of a given subnetwork affects only the relevant subset of samples. Finally, we apply L3D to a real-world transformer model and a convolutional neural network, demonstrating its potential to identify interpretable and relevant circuits in parameter space.

One way to avoid overfitting in machine learning is to use model parameters distributed according to a Bayesian posterior given the data, rather than the maximum likelihood estimator. Stochastic gradient Langevin dynamics (SGLD) is one algorithm to approximate such Bayesian posteriors for large models and datasets. SGLD is a standard stochastic gradient descent to which is added a controlled amount of noise, specifically scaled so that the parameter converges in law to the posterior distribution [WT11, TTV16]. The posterior predictive distribution can be approximated by an ensemble of samples from the trajectory. Choice of the variance of the noise is known to impact the practical behavior of SGLD: for instance, noise should be smaller for sensitive parameter directions. Theoretically, it has been suggested to use the inverse Fisher information matrix of the model as the variance of the noise, since it is also the variance of the Bayesian posterior [PT13, AKW12, GC11]. But the Fisher matrix is costly to compute for large- dimensional models. Here we use the easily computed Fisher matrix approximations for deep neural networks from [MO16, Oll15]. The resulting natural Langevin dynamics combines the advantages of Amari's natural gradient descent and Fisher-preconditioned Langevin dynamics for large neural networks. Small-scale experiments on MNIST show that Fisher matrix preconditioning brings SGLD close to dropout as a regularizing technique.