The difficulty in specifying rewards for many real world problems has led to an increased focus on learning rewards from human feedback, such as demonstrations. However, there are often many different reward functions that explain the human feedback, leaving agents with uncertainty over what the true reward function is. While most policy optimization approaches handle this uncertainty by optimizing for expected performance, many applications demand risk-averse behavior. We derive a novel policy gradient-style robust optimization approach, PG-BROIL, that optimizes a soft-robust objective that balances expected performance and risk. To the best of our knowledge, PG-BROIL is the first policy optimization algorithm robust to a distribution of reward hypotheses which can scale to continuous MDPs. Results suggest that PG-BROIL can produce a family of behaviors ranging from risk-neutral to risk-averse and outperforms state-of-the-art imitation learning algorithms when learning from ambiguous demonstrations by hedging against uncertainty, rather than seeking to uniquely identify the demonstrator’s reward function.
PC-PG: Policy Cover Directed Exploration for Provable Policy Gradient Learning
Direct policy gradient methods for reinforcement learning are a successful approach for a variety of reasons: they are model free, they directly optimize the performance metric of interest, and they allow for richly parameterized policies. Their primary drawback is that, by being local in nature, they fail to adequately explore the environment. In contrast, while model-based approaches and Q-learning can, at least in theory, directly handle exploration through the use of optimism, their ability to handle model misspecification and function approximation is far less evident. This work introduces the the POLICY COVER GUIDED POLICY GRADIENT (PC- PG) algorithm, which provably balances the exploration vs. exploitation tradeoff using an ensemble of learned policies (the policy cover). PC-PG enjoys polynomial sample complexity and run time for both tabular MDPs and, more generally, linear MDPs in an infinite dimensional RKHS. Furthermore, PC-PG also has strong guarantees under model misspecification that go beyond the standard worst case L infinity assumptions; these include approximation guarantees for state aggregation under an average case error assumption, along with guarantees under a more general assumption where the approximation error under distribution shift is controlled. We complement the theory with empirical evaluation across a variety of domains in both more »
- Award ID(s):
- 1703574
- Publication Date:
- NSF-PAR ID:
- 10276109
- Journal Name:
- Advances in neural information processing systems
- Issue:
- 33
- ISSN:
- 1049-5258
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We consider reinforcement learning (RL) in episodic MDPs with adversarial full-information reward feedback and unknown fixed transition kernels. We propose two model-free policy optimization algorithms, POWER and POWER++, and establish guarantees for their dynamic regret. Compared with the classical notion of static regret, dynamic regret is a stronger notion as it explicitly accounts for the non-stationarity of environments. The dynamic regret attained by the proposed algorithms interpolates between different regimes of non-stationarity, and moreover satisfies a notion of adaptive (near-)optimality, in the sense that it matches the (near-)optimal static regret under slow-changing environments. The dynamic regret bound features two components, one arising from exploration, which deals with the uncertainty of transition kernels, and the other arising from adaptation, which deals with non-stationary environments. Specifically, we show that POWER++ improves over POWER on the second component of the dynamic regret by actively adapting to non-stationarity through prediction. To the best of our knowledge, our work is the first dynamic regret analysis of model-free RL algorithms in non-stationary environments.
-
Abstract The softmax policy gradient (PG) method, which performs gradient ascent under softmax policy parameterization, is arguably one of the de facto implementations of policy optimization in modern reinforcement learning. For
$$\gamma $$ $${\mathcal {S}}$$ $$\frac{1}{1-\gamma }$$ $$\eta $$ $$\begin{aligned} \frac{1}{\eta } |{\mathcal {S}}|^{2^{\Omega \big (\frac{1}{1-\gamma }\big )}} ~\text {iterations} \end{aligned}$$ -
This paper studies a dynamic pricing problem under model misspecification. To characterize model misspecification, we adopt the ε-contamination model—the most fundamental model in robust statistics and machine learning. In particular, for a selling horizon of length T, the online ε-contamination model assumes that demands are realized according to a typical unknown demand function only for [Formula: see text] periods. For the rest of [Formula: see text] periods, an outlier purchase can happen with arbitrary demand functions. The challenges brought by the presence of outlier customers are mainly due to the fact that arrivals of outliers and their exhibited demand behaviors are completely arbitrary, therefore calling for robust estimation and exploration strategies that can handle any outlier arrival and demand patterns. We first consider unconstrained dynamic pricing without any inventory constraint. In this case, we adopt the Follow-the-Regularized-Leader algorithm to hedge against outlier purchase behavior. Then, we introduce inventory constraints. When the inventory is insufficient, we study a robust bisection-search algorithm to identify the clearance price—that is, the price at which the initial inventory is expected to clear at the end of T periods. Finally, we study the general dynamic pricing case, where a retailer has no clue whether the inventorymore »
-
We study the \emph{offline reinforcement learning} (offline RL) problem, where the goal is to learn a reward-maximizing policy in an unknown \emph{Markov Decision Process} (MDP) using the data coming from a policy $\mu$. In particular, we consider the sample complexity problems of offline RL for the finite horizon MDPs. Prior works derive the information-theoretical lower bounds based on different data-coverage assumptions and their upper bounds are expressed by the covering coefficients which lack the explicit characterization of system quantities. In this work, we analyze the \emph{Adaptive Pessimistic Value Iteration} (APVI) algorithm and derive the suboptimality upper bound that nearly matches $ O\left(\sum_{h=1}^H\sum_{s_h,a_h}d^{\pi^\star}_h(s_h,a_h)\sqrt{\frac{\mathrm{Var}_{P_{s_h,a_h}}{(V^\star_{h+1}+r_h)}}{d^\mu_h(s_h,a_h)}}\sqrt{\frac{1}{n}}\right). $ We also prove an information-theoretical lower bound to show this quantity is required under the weak assumption that $d^\mu_h(s_h,a_h)>0$ if $d^{\pi^\star}_h(s_h,a_h)>0$. Here $\pi^\star$ is a optimal policy, $\mu$ is the behavior policy and $d(s_h,a_h)$ is the marginal state-action probability. We call this adaptive bound the \emph{intrinsic offline reinforcement learning bound} since it directly implies all the existing optimal results: minimax rate under uniform data-coverage assumption, horizon-free setting, single policy concentrability, and the tight problem-dependent results. Later, we extend the result to the \emph{assumption-free} regime (where we make no assumption on $ \mu$) and obtain the assumption-free intrinsicmore »
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Publisher's Version of Record
- The DOI is not currently available
