Model-Based Reinforcement Learning with Value-Targeted Regression (2006.01107v1)

Abstract: This paper studies model-based reinforcement learning (RL) for regret minimization. We focus on finite-horizon episodic RL where the transition model $P$ belongs to a known family of models $\mathcal{P}$, a special case of which is when models in $\mathcal{P}$ take the form of linear mixtures: $P_{\theta} = \sum_{i=1}^{d} \theta_{i}P_{i}$. We propose a model based RL algorithm that is based on optimism principle: In each episode, the set of models that are `consistent' with the data collected is constructed. The criterion of consistency is based on the total squared error of that the model incurs on the task of predicting \emph{values} as determined by the last value estimate along the transitions. The next value function is then chosen by solving the optimistic planning problem with the constructed set of models. We derive a bound on the regret, which, in the special case of linear mixtures, the regret bound takes the form $\tilde{\mathcal{O}}(d\sqrt{H^{3}T})$, where $H$, $T$ and $d$ are the horizon, total number of steps and dimension of $\theta$, respectively. In particular, this regret bound is independent of the total number of states or actions, and is close to a lower bound $\Omega(\sqrt{HdT})$. For a general model family $\mathcal{P}$, the regret bound is derived using the notion of the so-called Eluder dimension proposed by Russo & Van Roy (2014).

• The paper introduces a novel model selection criterion that leverages value-targeted regression to construct confidence sets, enhancing exploration efficiency.
• It derives near-optimal theoretical regret bounds, with performance closely matching the lower bounds in linear mixture models.
• Experimental validations demonstrate UCRL-VTR's robust performance in challenging environments, highlighting its potential for sample-efficient learning.

An Analysis of Model-Based Reinforcement Learning with Value-Targeted Regression

The paper explores a model-based approach to reinforcement learning (RL) that incorporates value-targeted regression (VTR) in constructing confidence sets for optimistic planning. Reinforcement learning, concerned with learning how to act optimally in stochastic environments through trial and error, has seen significant advancements in model-free and model-based paradigms. This work explores model-based RL, where a model of the environment is learned alongside the optimal policy to minimize regret over repeated episodes.

Core Contributions

The paper's principal contribution is the introduction of a model selection criterion focused on the ability of prospective models to predict value functions rather than state transitions. This is encapsulated in the proposed UCRL-VTR algorithm, which constructs confidence sets based on VTR to enable robust optimistic exploration.

Some notable aspects of the research include:

1. Value-Targeted Regression: Instead of measuring consistency of a model based on transition predictions, VTR focuses on predicting the value functions associated with states. This narrows the model's learning to components critical to task performance and potentially lessens the degree of exploration needed.
2. Theoretical Regret Bounds: The paper derives theoretical bounds for the algorithm's regret. In the special case of linear mixture models, the regret scales as $\tilde{\mathcal{O}}(d \sqrt{H^3 T})$, where $d$ is the dimensionality of the parameter space, $H$ is the planning horizon, and $T$ the total time steps. This is close to the lower bound of $\Omega(\sqrt{HdT})$, signaling near-optimal performance.
3. Experimental Validation: The authors empirically validate the performance of UCRL-VTR across various benchmarks, demonstrating competitive or superior performance to baseline RL algorithms, particularly in environments where exploration is challenging.

Implications

The use of VTR for building confidence sets marks a distinct shift in focus towards learning models that directly aid in policy optimization rather than comprehensive environmental modeling. This has practical implications for model-based RL in environments with high-dimensional state spaces, where completely modeling transition dynamics is computationally infeasible.

Moreover, the research aligns with the notion that RL models can benefit from aligning more closely with the ultimate objective—regret minimization. Such an approach can lead to more sample-efficient learning, which is crucial for real-world applications where data collection can be costly or time-consuming.

Theoretical and Practical Extensions

The theoretical framework offered by this work can be extended to other forms of function approximation beyond linear models, which will be crucial for addressing broader classes of RL problems. Exploring non-linear or deep learning-based function approximators could potentially capture more complex dynamics and further reduce regret and computational overhead.

Practically, future work might focus on integrating mixed objectives, where elements of both VTR and traditional transition prediction could be utilized to further minimize regret while ensuring robustness across a variety of environments. These aspects underline the potential for more granular, fine-tuned control over the balance between exploration and exploitation in model-based RL.

In conclusion, the paper presents a refined approach to model-based RL, emphasizing value prediction in model construction and promising strides in reducing regret through focused exploration strategies. This insight is pivotal for advancing RL towards more efficient, realistic deployments in complex domains.