MDPs and Bellman equations through deep RL, imitation learning, and Sim-to-Real, always tied to robot applications.
This is an editorially selected reading order. Begin at step 1 or go directly to the topic you need.
Reinforcement learning is a closed loop in which an agent chooses actions from observations and maximizes delayed rewards. This primer explains MDPs, value functions, policies, Bellman equations, exploration versus exploitation, reward design, and the path from simulation to a real robot.
Q-learning updates action values with the Bellman optimality target. This primer follows the path from a tabular Q-table to a Deep Q-Network, explaining experience replay, target networks, overestimation, and safe placement in a robot stack.
Policy gradients update a policy directly so that steering, thrust, and joint torque can remain continuous. This article connects Actor-Critic, PPO, and SAC, then covers clipping, entropy regularization, evaluation, and the safety boundary for Sim-to-Real transfer.
In reinforcement learning implementations, reward-function design more often determines the outcome than the algorithm does. This article organizes sparse vs. dense reward, the policy invariance of potential-based reward shaping, real cases of reward hacking, inverse reinforcement learning, and constrained RL.
World models, prediction error, MPC, domain randomization, system identification, and safety monitoring for real machines.
Behavior Cloning, DAgger, and inverse reinforcement learning use demonstrations when rewards are hard to write. This primer covers covariate shift, reward inference, VLA connections, evaluation, safety, and data provenance.
A source-based technical guide to Physical Intelligence's π0: the PaliGemma VLM and dedicated Action Expert, continuous action generation with conditional flow matching, cross-embodiment training across seven robot types, and the difference from autoregressive VLA models such as RT-2 and OpenVLA.
When multiple agents learn at the same time, a single-agent MDP no longer holds. This article organizes non-stationarity, cooperative/competitive/mixed settings, CTDE, the credit-assignment problem, and MADDPG and QMIX, with equations and diagrams.