Sentiment-Driven Agents

• Sentiment-driven agents are autonomous systems that integrate affective signals into decision-making by coupling latent sentiment representations with dynamic policies.
• They employ mathematical models such as coupled ODEs to link sentiment functions with agent behaviors, capturing nuances like order flow and price volatility.
• Applications span algorithmic trading and adaptive human-computer interaction, though effective deployment requires robust sentiment estimation and calibration.

A sentiment-driven agent is an autonomous or semi-autonomous system that extracts, models, and responds to affective signals—typically representing collective or individual emotional stances—in order to inform, guide, or optimize its decision-making and action selection. Such agents have emerged across domains including financial markets, human-computer interaction, and reinforcement learning, with implementations that range from explicit mathematical modeling of investor sentiment to multimodal analysis of affect in human conversation.

1. Fundamental Principles of Sentiment-Driven Agents

Sentiment-driven agents are characterized by their endogenous or exogenous incorporation of sentiment signals into their internal state, action selection, and adaptation strategies. The core architectural principle is the coupling of a sentiment representation—either as an explicit function (e.g., slow-changing latent variable) or as an inferred, data-driven quantity—with the agent's policy and environment dynamics.

An illustrative instantiation is provided in (Lykov et al., 2012), where market agents (bulls, bears) are endowed with “sentiment functions” $L(t)$ and $M(t)$, measuring their conception of the fair price. These functions both drive order-submission intensities and evolve recursively in response to trading activity and exogenous news shocks:

• Bulls submit buy orders at intensity %%%%2%%%%
• Bears submit sell orders at intensity $\mu_n(t) = \exp\{c(n-M(t))\}$

The sentiment variables are not directly measurable in real time; they form a latent, slowly varying environment observed indirectly via order book reactions and price/volume statistics.

The general paradigm is equally applicable in other domains where sentiment is derived not from explicit event-driven updates, but rather from statistical models of language, multimodal data, or reinforcement feedback.

2. Dynamical Modeling and Coupling of Sentiment and Agent Behavior

A distinctive technical feature of sophisticated sentiment-driven agents is the explicit dynamical system linking sentiment evolution and agent/environment behavior.

In the continuous double auction model (Lykov et al., 2012), the sentiment dynamics are governed by a pair of coupled ordinary differential equations (ODEs), with the evolution of $L(t)$ and $M(t)$ depending on both agent activity and external news: $$L'(t) = -\sum_n \lambda_n(t) p_n(t) + C_\lambda + \sum_k A_k \delta(t - \tau_k)$$

$$M'(t) = \sum_n \mu_n(t) p_n(t) - C_\mu - \sum_k B_k \delta(t - \theta_k)$$

Here, $p_n(t)$ is the distribution over price levels, and the $\delta$-functions model instantaneous jumps associated with news. Baseline rates $C_\lambda$, $C_\mu$ embody persistent trading intensities.

The fast price process $x(t)$ is influenced by these sentiment variables, producing a nonlinear Markov process $X(t) = (x(t), L(t), M(t))$ exhibiting long-term statistical dependencies and feedback loops.

In the diffusion limit, the price dynamics approach an Ornstein–Uhlenbeck process with state-dependent volatility: $$dX(t) = e^{(L(t)-M(t))/2} \, [dw(t) - 2(X(t) - (L(t)+M(t))/2)dt]$$ with the volatility term $e^{(L(t)-M(t))/2}$ exponentially sensitive to the disparity in sentiment.

3. Mechanisms for Sentiment Measurement and Estimation

The agent’s access to sentiment can occur through embedded modeling (e.g., latent ODE states) or through statistical inference from available market or behavioral data. While (Lykov et al., 2012) prescribes unobservable, latent sentiment variables, it is shown that these can be estimated a posteriori via historical price and volume data—rendering the agent’s sentiment state reconstructible and actionable for algorithmic trading.

Alternative approaches in sentiment-driven RL or conversational agents (for example, in (Deshpande et al., 2020) and related literature) measure sentiment extrinsically by applying lexicon-based or neural models to natural language, extracting a polarity score or emotion class that is then mapped to internal signal or reward. These methods enable the construction of agents that “sense” affective shifts from text, order flow, or multimodal signals, turning them into quantitative cues for subsequent action.

4. Policy Adaptation and Sentiment Feedback

Sentiment-driven agents not only sense or infer sentiment; they adapt their policies in accordance with its evolution, typically via mechanisms sensitive to latent state, observed emotion, or derivatives thereof.

In (Lykov et al., 2012), the impact of sentiment on market microstructure appears directly via the action intensities and the (sentiment-dependent) volatility. Notably, periods of acute sentiment disagreement ($|L(t) - M(t)|$ large) induce high volatility, amplifying both order flow and price moves—a feature aligned with empirical bursts observed during news shocks and stress periods.

The ODEs for $L(t)$ and $M(t)$ further predict gradual decay of sentiment disagreement (e.g., via $L'(t) = -e^{L(t)-M(t)}+1$, $M'(t) = e^{L(t)-M(t)}-1$), an endogenous mean reversion property offering an explanation for observed volatility clustering in markets.

This coupling enables both the simulation of observed price dynamics and the design of trading strategies that exploit, or hedge, forecastable shifts in collective mood.

5. Practical Implications and Agent-Based Market Modeling

The explicit modeling of sentiment within agents allows for the generation of microstructural properties—such as V-shaped order books, the genesis of sudden price jumps, and realistic long-memory phenomena—as endogenously arising from the interplay between agent behavior and sentiment feedback loops.

Key implications, as established in (Lykov et al., 2012), are:

• Sudden news-driven sentiment shifts (increment or decrement of $L(t)$ or $M(t)$) can generate order flow avalanches, aligning with empirical spikes in trading volume and directional moves.
• Disagreement among investors, operationalized by the magnitude $|L(t) - M(t)|$, is a primary driver of market instability and transient volatility.
• Latent sentiment functions provide a foundation for real-time estimation and adaptive agent policy design, opening the pathway for sentiment-aware algorithmic trading and hedging strategies that are responsive to both observed and inferred shifts in market tone.

The model’s continuum limit connects the discrete agent view to stochastic process theory, explicitly relating sentiment to mean-reverting yet volatile price evolution—a crucial feature for risk modeling and derivative pricing.

6. Comparative Outlook and Generalization

While the specific formalisms of (Lykov et al., 2012) pertain to order book dynamics, the paradigm of sentiment-driven agency extends to a broad spectrum of multi-agent and single-agent environments. The structural approach—coupling slow (sentiment, belief) and fast (action, environment state) variables through observation, inference, and feedback—recurs in dialog systems, reinforcement learning with affective rewards, and market simulation models.

In all contexts, the essential concept is that agent behavior is dynamically informed by the agent’s or collective’s evolving representation of affective or belief-driven state, with the dual effect that sentiment both shapes the environment and is, in turn, recursively modified by it.

Component	Mathematical Expression	Interpretation
Order Rates	$\lambda_n(t) = e^{-c(n - L(t))}$; $\mu_n(t) = e^{c(n - M(t))}$	Sentiment-dependent buy/sell order intensities
Sentiment ODEs	$$L'(t) = -\sum_n \lambda_n(t)p_n(t) + C_\lambda + \sum_k A_k\delta(t - \tau_k)$$	Bulls' sentiment driven by order flow and news
Volatility (diffusion limit)	$e^{(L(t)-M(t))/2}$	Instantaneous volatility as function of sentiment discrepancy
Mean Reversion Point	$(L(t) + M(t))/2$	Latent fair price arising from average sentiment

The theoretical results justify the integration of sentiment measurements into both agent-based simulation and systematic policy development, with particular efficacy in complex adaptive environments characterized by substantial information flows and feedback effects.

7. Limitations and Further Directions

While sentiment-driven agent architectures enable the reproduction of critical market stylized facts and adaptive policy behaviors, several limitations persist:

• Sentiment functions ($L(t)$, $M(t)$) are latent and require robust inference for use in empirical applications.
• The functional forms (exponential sensitivity, linear ODEs) depend on calibration constants ($c$, $C_\lambda$, $C_\mu$) whose selection affects the system’s stability and realism.
• The model, as stated in (Lykov et al., 2012), provides a natural, but not exclusive, explanation for volatility clustering and order flow avalanches; real-world systems may require additional heterogeneity and complexity (multiple sentiment groups, memory effects, bounded rationality).

Future enhancements may include richer microstructural agent designs, finer modeling of news impact (distribution of jump amplitudes), and integration with contemporary sentiment estimation methods from natural language processing and real-time data mining. Advanced sentiment-driven agents are likely to feature dynamic learning of functional parameters from high-frequency data, enabling adaptive behaviors that more closely track non-stationary, multi-source collective sentiment in complex social and economic systems.