We present a simple model of a non-equilibrium self-organizing market where asset prices are partially driven by investment decisions of a bounded-rational agent. The agent acts in a stochastic market environment driven by various exogenous "alpha" signals, agent's own actions (via market impact), and noise. Unlike traditional agent-based models, our agent aggregates all traders in the market, rather than being a representative agent. Therefore, it can be identified with a bounded-rational component of the market itself, providing a particular implementation of an Invisible Hand market mechanism. In such setting, market dynamics are modeled as a fictitious self-play of such bounded-rational market-agent in its adversarial stochastic environment. As rewards obtained by such self-playing market agent are not observed from market data, we formulate and solve a simple model of such market dynamics based on a neuroscience-inspired Bounded Rational Information Theoretic Inverse Reinforcement Learning (BRIT-IRL). This results in effective asset price dynamics with a non-linear mean reversion - which in our model is generated dynamically, rather than being postulated. We argue that our model can be used in a similar way to the Black-Litterman model. In particular, it represents, in a simple modeling framework, market views of common predictive signals, market impacts and implied optimal dynamic portfolio allocations, and can be used to assess values of private signals. Moreover, it allows one to quantify a "market-implied" optimal investment strategy, along with a measure of market rationality. Our approach is numerically light, and can be implemented using standard off-the-shelf software such as TensorFlow.
An adversarial interpretation of Information Theoretic Bounded Rationality was suggested in @cite_54 where it was shown that a single-agent free energy optimization is equivalent to a fictitious game between an agent and an imaginary adversary. In our model, we have a similar setting, where an agent representing a bounded-rational component of the market optimizes its free energy. The optimization amounts to a dynamical optimization of agent's portfolio in a stochastic market environment with information processing costs. The latter are expressed as an entropy regularization of a value function, see below. As will be shown in Sect. , using the method of @cite_54 , such self-play can be equivalently viewed as adversarial learning in a fictitious two-party game with an adversarial opponent.
@cite_54
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Recently, there has been a growing interest in modeling planning with information constraints. Accordingly, an agent maximizes a regularized expected utility known as the free energy, where the regularizer is given by the information divergence from a prior to a posterior policy. While this approach can be justified in various ways, including from statistical mechanics and information theory, it is still unclear how it relates to decision-making against adversarial environments. This connection has previously been suggested in work relating the free energy to risk-sensitive control and to extensive form games. Here, we show that a single-agent free energy optimization is equivalent to a game between the agent and an imaginary adversary. The adversary can, by paying an exponential penalty, generate costs that diminish the decision maker's payoffs. It turns out that the optimal strategy of the adversary consists in choosing costs so as to render the decision maker indifferent among its choices, which is a definining property of a Nash equilibrium, thus tightening the connection between free energy optimization and game theory. In this paper, we describe a method to represent and discover adversarial group behavior in a continuous domain. In comparison to other types of behavior, adversarial behavior is heavily structured as the location of a player (or agent) is dependent both on their teammates and adversaries, in addition to the tactics or strategies of the team. We present a method which can exploit this relationship through the use of a spatiotemporal basis model. As players constantly change roles during a match, we show that employing a "role-based" representation instead of one based on player "identity" can best exploit the playing structure. As vision-based systems currently do not provide perfect detection tracking (e.g. missed or false detections), we show that our compact representation can effectively "denoise" erroneous detections as well as enabling temporal analysis, which was previously prohibitive due to the dimensionality of the signal. To evaluate our approach, we used a fully instrumented field-hockey pitch with 8 fixed high-definition (HD) cameras and evaluated our approach on approximately 200,000 frames of data from a state-of-the-art real-time player detector and compare it to manually labelled data. In this semi-tutorial paper, we first review the information-theoretic approach to account for the computational costs incurred during the search for optimal actions in a sequential decision-making problem. The traditional (MDP) framework ignores computational limitations while searching for optimal policies, essentially assuming that the acting agent is perfectly rational and aims for exact optimality. Using the free-energy, a variational principle is introduced that accounts not only for the value of a policy alone, but also considers the cost of finding this optimal policy. The solution of the variational equations arising from this formulation can be obtained using familiar Bellman-like value iterations from dynamic programming (DP) and the Blahut-Arimoto (BA) algorithm from rate distortion theory. Finally, we demonstrate the utility of the approach for generating hierarchies of state abstractions that can be used to best exploit the available computational resources. A numerical example showcases these concepts for a path-planning problem in a grid world environment. We introduce two tactics to attack agents trained by deep reinforcement learning algorithms using adversarial examples, namely the strategically-timed attack and the enchanting attack. In the strategically-timed attack, the adversary aims at minimizing the agent's reward by only attacking the agent at a small subset of time steps in an episode. Limiting the attack activity to this subset helps prevent detection of the attack by the agent. We propose a novel method to determine when an adversarial example should be crafted and applied. In the enchanting attack, the adversary aims at luring the agent to a designated target state. This is achieved by combining a generative model and a planning algorithm: while the generative model predicts the future states, the planning algorithm generates a preferred sequence of actions for luring the agent. A sequence of adversarial examples is then crafted to lure the agent to take the preferred sequence of actions. We apply the two tactics to the agents trained by the state-of-the-art deep reinforcement learning algorithm including DQN and A3C. In 5 Atari games, our strategically timed attack reduces as much reward as the uniform attack (i.e., attacking at every time step) does by attacking the agent 4 times less often. Our enchanting attack lures the agent toward designated target states with a more than 70 success rate. Videos are available at this http URL