Deep Reinforcement Learning for Stock Portfolio Optimization

Stock portfolio optimization is the process of constant re-distribution of money to a pool of various stocks. In this paper, we will formulate the problem such that we can apply Reinforcement Learning for the task properly. To maintain a realistic assumption about the market, we will incorporate transaction cost and risk factor into the state as well. On top of that, we will apply various state-of-the-art Deep Reinforcement Learning algorithms for comparison. Since the action space is continuous, the realistic formulation were tested under a family of state-of-the-art continuous policy gradients algorithms: Deep Deterministic Policy Gradient (DDPG), Generalized Deterministic Policy Gradient (GDPG) and Proximal Policy Optimization (PPO), where the former two perform much better than the last one. Next, we will present the end-to-end solution for the task with Minimum Variance Portfolio Theory for stock subset selection, and Wavelet Transform for extracting multi-frequency data pattern. Observations and hypothesis were discussed about the results, as well as possible future research directions.

Deterministic Policy Gradients With General State Transitions

We study a reinforcement learning setting, where the state transition function is a convex combination of a stochastic continuous function and a deterministic function. Such a setting generalizes the widely-studied stochastic state transition setting, namely the setting of deterministic policy gradient (DPG). We firstly give a simple example to illustrate that the deterministic policy gradient may be infinite under deterministic state transitions, and introduce a theoretical technique to prove the existence of the policy gradient in this generalized setting. Using this technique, we prove that the deterministic policy gradient indeed exists for a certain set of discount factors, and further prove two conditions that guarantee the existence for all discount factors. We then derive a closed form of the policy gradient whenever exists. Furthermore, to overcome the challenge of high sample complexity of DPG in this setting, we propose the Generalized Deterministic Policy Gradient (GDPG) algorithm. The main innovation of the algorithm is a new method of applying model-based techniques to the model-free algorithm, the deep deterministic policy gradient algorithm (DDPG). GDPG optimize the long-term rewards of the model-based augmented MDP subject to a constraint that the long-rewards of the MDP is less than the original one. We finally conduct extensive experiments comparing GDPG with state-of-the-art methods and the direct model-based extension method of DDPG on several standard continuous control benchmarks. Results demonstrate that GDPG substantially outperforms DDPG, the model-based extension of DDPG and other baselines in terms of both convergence and long-term rewards in most environments

Gradient Estimation Using Stochastic Computation Graphs

In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external world. Estimating the gradient of this loss function, using samples, lies at the core of gradient-based learning algorithms for these problems. We introduce the formalism of stochastic computation graphs---directed acyclic graphs that include both deterministic functions and conditional probability distributions---and describe how to easily and automatically derive an unbiased estimator of the loss function's gradient. The resulting algorithm for computing the gradient estimator is a simple modification of the standard backpropagation algorithm. The generic scheme we propose unifies estimators derived in variety of prior work, along with variance-reduction techniques therein. It could assist researchers in developing intricate models involving a combination of stochastic and deterministic operations, enabling, for example, attention, memory, and control actions.Comment: Advances in Neural Information Processing Systems 28 (NIPS 2015

A Multiagent Reinforcement Learning Algorithm with Non-linear Dynamics

Several multiagent reinforcement learning (MARL) algorithms have been proposed to optimize agents decisions. Due to the complexity of the problem, the majority of the previously developed MARL algorithms assumed agents either had some knowledge of the underlying game (such as Nash equilibria) and/or observed other agents actions and the rewards they received. We introduce a new MARL algorithm called the Weighted Policy Learner (WPL), which allows agents to reach a Nash Equilibrium (NE) in benchmark 2-player-2-action games with minimum knowledge. Using WPL, the only feedback an agent needs is its own local reward (the agent does not observe other agents actions or rewards). Furthermore, WPL does not assume that agents know the underlying game or the corresponding Nash Equilibrium a priori. We experimentally show that our algorithm converges in benchmark two-player-two-action games. We also show that our algorithm converges in the challenging Shapleys game where previous MARL algorithms failed to converge without knowing the underlying game or the NE. Furthermore, we show that WPL outperforms the state-of-the-art algorithms in a more realistic setting of 100 agents interacting and learning concurrently. An important aspect of understanding the behavior of a MARL algorithm is analyzing the dynamics of the algorithm: how the policies of multiple learning agents evolve over time as agents interact with one another. Such an analysis not only verifies whether agents using a given MARL algorithm will eventually converge, but also reveals the behavior of the MARL algorithm prior to convergence. We analyze our algorithm in two-player-two-action games and show that symbolically proving WPLs convergence is difficult, because of the non-linear nature of WPLs dynamics, unlike previous MARL algorithms that had either linear or piece-wise-linear dynamics. Instead, we numerically solve WPLs dynamics differential equations and compare the solution to the dynamics of previous MARL algorithms

Learning robust control for LQR systems with multiplicative noise via policy gradient

The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all recent work in this area, we consider multiplicative noise models, which are increasingly relevant because they explicitly incorporate inherent uncertainty and variation in the system dynamics and thereby improve robustness properties of the controller. Robustness is a critical and poorly understood issue in reinforcement learning; existing methods which do not account for uncertainty can converge to fragile policies or fail to converge at all. Additionally, intentional injection of multiplicative noise into learning algorithms can enhance robustness of policies, as observed in ad hoc work on domain randomization. Although policy gradient algorithms require optimization of a non-convex cost function, we show that the multiplicative noise LQR cost has a special property called gradient domination, which is exploited to prove global convergence of policy gradient algorithms to the globally optimum control policy with polynomial dependence on problem parameters. Results are provided both in the model-known and model-unknown settings where samples of system trajectories are used to estimate policy gradients

Backprop-Q: Generalized Backpropagation for Stochastic Computation Graphs

In real-world scenarios, it is appealing to learn a model carrying out stochastic operations internally, known as stochastic computation graphs (SCGs), rather than learning a deterministic mapping. However, standard backpropagation is not applicable to SCGs. We attempt to address this issue from the angle of cost propagation, with local surrogate costs, called Q-functions, constructed and learned for each stochastic node in an SCG. Then, the SCG can be trained based on these surrogate costs using standard backpropagation. We propose the entire framework as a solution to generalize backpropagation for SCGs, which resembles an actor-critic architecture but based on a graph. For broad applicability, we study a variety of SCG structures from one cost to multiple costs. We utilize recent advances in reinforcement learning (RL) and variational Bayes (VB), such as off-policy critic learning and unbiased-and-low-variance gradient estimation, and review them in the context of SCGs. The generalized backpropagation extends transported learning signals beyond gradients between stochastic nodes while preserving the benefit of backpropagating gradients through deterministic nodes. Experimental suggestions and concerns are listed to help design and test any specific model using this framework.Comment: NeurIPS 2018 Deep Reinforcement Learning Worksho

Merging Deterministic Policy Gradient Estimations with Varied Bias-Variance Tradeoff for Effective Deep Reinforcement Learning

Deep reinforcement learning (DRL) on Markov decision processes (MDPs) with continuous action spaces is often approached by directly training parametric policies along the direction of estimated policy gradients (PGs). Previous research revealed that the performance of these PG algorithms depends heavily on the bias-variance tradeoffs involved in estimating and using PGs. A notable approach towards balancing this tradeoff is to merge both on-policy and off-policy gradient estimations. However existing PG merging methods can be sample inefficient and are not suitable to train deterministic policies directly. To address these issues, this paper introduces elite PGs and strengthens their variance reduction effect by adopting elitism and policy consolidation techniques to regularize policy training based on policy behavioral knowledge extracted from elite trajectories. Meanwhile, we propose a two-step method to merge elite PGs and conventional PGs as a new extension of the conventional interpolation merging method. At both the theoretical and experimental levels, we show that both two-step merging and interpolation merging can induce varied bias-variance tradeoffs during policy training. They enable us to effectively use elite PGs and mitigate their performance impact on trained policies. Our experiments also show that two-step merging can outperform interpolation merging and several state-of-the-art algorithms on six benchmark control tasks

Simultaneous Perturbation Methods for Adaptive Labor Staffing in Service Systems

Service systems are labor intensive due to the large variation in the tasks required to address service requests from multiple customers. Aligning the staffing levels to the forecasted workloads adaptively in such systems is nontrivial because of a large number of parameters and operational variations leading to a huge search space. A challenging problem here is to optimize the staffing while maintaining the system in steady-state and compliant to aggregate service level agreement (SLA) constraints. Further, because these parameters change on a weekly basis, the optimization should not take longer than a few hours. We formulate this problem as a constrained Markov cost process parameterized by the (discrete) staffing levels. We propose novel simultaneous perturbation stochastic approximation (SPSA) based SASOC (Staff Allocation using Stochastic Optimization with Constraints) algorithms for solving the above problem. The algorithms include both first order as well as second order methods and incorporate SPSA based gradient estimates in the primal, with dual ascent for the Lagrange multipliers. Both the algorithms that we propose are online, incremental and easy to implement. Further, they involve a certain generalized smooth projection operator, which is essential to project the continuous-valued worker parameter tuned by SASOC algorithms onto the discrete set. We validated our algorithms on five real-life service systems and compared them with a state-of-the-art optimization tool-kit OptQuest. Being 25 times faster than OptQuest, our algorithms are particularly suitable for adaptive labor staffing. Also, we observe that our algorithms guarantee convergence and find better solutions than OptQuest in many cases

OffCon3^3: What is state of the art anyway?

Two popular approaches to model-free continuous control tasks are SAC and TD3. At first glance these approaches seem rather different; SAC aims to solve the entropy-augmented MDP by minimising the KL-divergence between a stochastic proposal policy and a hypotheical energy-basd soft Q-function policy, whereas TD3 is derived from DPG, which uses a deterministic policy to perform policy gradient ascent along the value function. In reality, both approaches are remarkably similar, and belong to a family of approaches we call `Off-Policy Continuous Generalized Policy Iteration'. This illuminates their similar performance in most continuous control benchmarks, and indeed when hyperparameters are matched, their performance can be statistically indistinguishable. To further remove any difference due to implementation, we provide OffCon$^3$ (Off-Policy Continuous Control: Consolidated), a code base featuring state-of-the-art versions of both algorithms

Adaptive Algorithms for Coverage Control and Space Partitioning in Mobile Robotic Networks

This paper considers deployment problems where a mobile robotic network must optimize its configuration in a distributed way in order to minimize a steady-state cost function that depends on the spatial distribution of certain probabilistic events of interest. Moreover, it is assumed that the event location distribution is a priori unknown, and can only be progressively inferred from the observation of the actual event occurrences. Three classes of problems are discussed in detail: coverage control problems, spatial partitioning problems, and dynamic vehicle routing problems. In each case, distributed stochastic gradient algorithms optimizing the performance objective are presented. The stochastic gradient view simplifies and generalizes previously proposed solutions, and is applicable to new complex scenarios, such as adaptive coverage involving heterogeneous agents. Remarkably, these algorithms often take the form of simple distributed rules that could be implemented on resource-limited platforms.Comment: 16 pages, 4 figures. Long version of a manuscript to appear in the Transactions on Automatic Contro