Towards Provable Log Density Policy Gradient

Policy gradient methods are a vital ingredient behind the success of modern reinforcement learning. Modern policy gradient methods, although successful, introduce a residual error in gradient estimation. In this work, we argue that this residual term is significant and correcting for it could potentially improve sample-complexity of reinforcement learning methods. To that end, we propose log density gradient to estimate the policy gradient, which corrects for this residual error term. Log density gradient method computes policy gradient by utilising the state-action discounted distributional formulation. We first present the equations needed to exactly find the log density gradient for a tabular Markov Decision Processes (MDPs). For more complex environments, we propose a temporal difference (TD) method that approximates log density gradient by utilizing backward on-policy samples. Since backward sampling from a Markov chain is highly restrictive we also propose a min-max optimization that can approximate log density gradient using just on-policy samples. We also prove uniqueness, and convergence under linear function approximation, for this min-max optimization. Finally, we show that the sample complexity of our min-max optimization to be of the order of $m^{-1/2}$, where $m$ is the number of on-policy samples. We also demonstrate a proof-of-concept for our log density gradient method on gridworld environment, and observe that our method is able to improve upon the classical policy gradient method by a clear margin, thus indicating a promising novel direction to develop reinforcement learning algorithms that require fewer samples.

Marginalized Importance Sampling for Off-Environment Policy Evaluation

Reinforcement Learning (RL) methods are typically sample-inefficient, making it challenging to train and deploy RL-policies in real world robots. Even a robust policy trained in simulation, requires a real-world deployment to assess their performance. This paper proposes a new approach to evaluate the real-world performance of agent policies without deploying them in the real world. The proposed approach incorporates a simulator along with real-world offline data to evaluate the performance of any policy using the framework of Marginalized Importance Sampling (MIS). Existing MIS methods face two challenges: (1) large density ratios that deviate from a reasonable range and (2) indirect supervision, where the ratio needs to be inferred indirectly, thus exacerbating estimation error. Our approach addresses these challenges by introducing the target policy's occupancy in the simulator as an intermediate variable and learning the density ratio as the product of two terms that can be learned separately. The first term is learned with direct supervision and the second term has a small magnitude, thus making it easier to run. We analyze the sample complexity as well as error propagation of our two step-procedure. Furthermore, we empirically evaluate our approach on Sim2Sim environments such as Cartpole, Reacher and Half-Cheetah. Our results show that our method generalizes well across a variety of Sim2Sim gap, target policies and offline data collection policies. We also demonstrate the performance of our algorithm on a Sim2Real task of validating the performance of a 7 DOF robotic arm using offline data along with a gazebo based arm simulator.

Equivariant Few-Shot Learning from Pretrained Models

Efficient transfer learning algorithms are key to the success of foundation models on diverse downstream tasks even with limited data. Recent works of \cite{basu2022equi} and \cite{kaba2022equivariance} propose group averaging (\textit{equitune}) and optimization-based methods, respectively, over features from group-transformed inputs to obtain equivariant outputs from non-equivariant neural networks. While \cite{kaba2022equivariance} are only concerned with training from scratch, we find that equitune performs poorly on equivariant zero-shot tasks despite good finetuning results. We hypothesize that this is because pretrained models provide better quality features for certain transformations than others and simply averaging them is deleterious. Hence, we propose $\lambda$-\textit{equitune} that averages the features using \textit{importance weights}, $\lambda$s. These weights are learned directly from the data using a small neural network, leading to excellent zero-shot and finetuned results that outperform equitune. Further, we prove that $\lambda$-equitune is equivariant and a universal approximator of equivariant functions. Additionally, we show that the method of \cite{kaba2022equivariance} used with appropriate loss functions, which we call \textit{equizero}, also gives excellent zero-shot and finetuned performance. Both equitune and equizero are special cases of $\lambda$-equitune. To show the simplicity and generality of our method, we validate on a wide range of diverse applications and models such as 1) image classification using CLIP, 2) deep Q-learning, 3) fairness in natural language generation (NLG), 4) compositional generalization in languages, and 5) image classification using pretrained CNNs such as Resnet and Alexnet.

Off Environment Evaluation Using Convex Risk Minimization

Applying reinforcement learning (RL) methods on robots typically involves training a policy in simulation and deploying it on a robot in the real world. Because of the model mismatch between the real world and the simulator, RL agents deployed in this manner tend to perform suboptimally. To tackle this problem, researchers have developed robust policy learning algorithms that rely on synthetic noise disturbances. However, such methods do not guarantee performance in the target environment. We propose a convex risk minimization algorithm to estimate the model mismatch between the simulator and the target domain using trajectory data from both environments. We show that this estimator can be used along with the simulator to evaluate performance of an RL agents in the target domain, effectively bridging the gap between these two environments. We also show that the convergence rate of our estimator to be of the order of ${n^{-1/4}}$, where $n$ is the number of training samples. In simulation, we demonstrate how our method effectively approximates and evaluates performance on Gridworld, Cartpole, and Reacher environments on a range of policies. We also show that the our method is able to estimate performance of a 7 DOF robotic arm using the simulator and remotely collected data from the robot in the real world.