  We present a reinforcement learning approach to goal based wealth management
problems such as optimization of retirement plans or target dated funds. In
such problems, an investor seeks to achieve a financial goal by making periodic
investments in the portfolio while being employed, and periodically draws from
the account when in retirement, in addition to the ability to re-balance the
portfolio by selling and buying different assets (e.g. stocks). Instead of
relying on a utility of consumption, we present G-Learner: a reinforcement
learning algorithm that operates with explicitly defined one-step rewards, does
not assume a data generation process, and is suitable for noisy data. Our
approach is based on G-learning - a probabilistic extension of the Q-learning
method of reinforcement learning.
  In this paper, we demonstrate how G-learning, when applied to a quadratic
reward and Gaussian reference policy, gives an entropy-regulated Linear
Quadratic Regulator (LQR). This critical insight provides a novel and
computationally tractable tool for wealth management tasks which scales to high
dimensional portfolios. In addition to the solution of the direct problem of
G-learning, we also present a new algorithm, GIRL, that extends our goal-based
G-learning approach to the setting of Inverse Reinforcement Learning (IRL)
where rewards collected by the agent are not observed, and should instead be
inferred. We demonstrate that GIRL can successfully learn the reward parameters
of a G-Learner agent and thus imitate its behavior. Finally, we discuss
potential applications of the G-Learner and GIRL algorithms for wealth
management and robo-advising.
