The Conditional Sequence Modeling (CSM) paradigm, benefiting from the transformer's powerful distribution modeling capabilities, has demonstrated considerable promise in Reinforcement Learning (RL) tasks. However, much of the work has focused on applying CSM to single online or offline settings, with the general architecture rarely explored. Additionally, existing methods primarily focus on deterministic trajectory modeling, overlooking the randomness of state transitions and the diversity of future trajectory distributions. Fortunately, value-based methods offer a viable solution for CSM, further bridging the potential gap between offline and online RL. In this paper, we propose Value-Guided Decision Transformer (VDT), which leverages value functions to perform advantage-weighting and behavior regularization on the Decision Transformer (DT), guiding the policy toward upper-bound optimal decisions during the offline training phase.

The practical use of reinforcement learning (RL) requires handling diverse settings, including online, offline, and offline-to-online learning. Instead of developing separate algorithms for each setting, we propose Uni-RL, a unified model-free RL framework that addresses all these scenarios within a single formulation. Uni-RL builds on the Implicit Value Regularization (IVR) framework and generalizes its dataset behavior constraint to the constraint w.r.t a reference policy, yielding an unified value learning objective for general settings. The reference policy is chosen to be the target policy in the online setting and the behavior policy in the offline setting. Using an iteratively refined behavior policy solves the over-constrained problem of directly applying IVR in the online setting, it provides an implicit trust-region style update through the value function while being off-policy.

We provide faster randomized algorithms for computing an $\epsilon$-optimal policy in a discounted Markov decision process with $A_{\text{tot}}$-state-action pairs, bounded rewards, and discount factor $\gamma$.

Matrix completion, where we wish to recover a low rank matrix by observing a few entries from it, is a widely studied problem in both theory and practice with wide applications. Most of the provable algorithms so far on this problem have been restricted to the offline setting where they provide an estimate of the unknown matrix using all observations simultaneously. However, in many applications, the online version, where we observe one entry at a time and dynamically update our estimate, is more appealing. While existing algorithms are efficient for the offline setting, they could be highly inefficient for the online setting. In this paper, we propose the first provable, efficient online algorithm for matrix completion. Our algorithm starts from an initial estimate of the matrix and then performs non-convex stochastic gradient descent (SGD). After every observation, it performs a fast update involving only one row of two tall matrices, giving near linear total runtime. Our algorithm can be naturally used in the offline setting as well, where it gives competitive sample complexity and runtime to state of the art algorithms. Our proofs introduce a general framework to show that SGD updates tend to stay away from saddle surfaces and could be of broader interests to other non-convex problems.