def METHOD_NAME(config: dict[Any, Any]) -> None:
    """
    Initialize logging using the "old-style" configuration scheme, e.g.:
        {
        'logging': {
            'distributed': 'info',
            'tornado': 'critical',
            'tornado.application': 'error',
            }
        }
    """
    loggers: dict[str, str | int] = {  # default values
        "distributed": "info",
        "distributed.client": "warning",
        "bokeh": "error",
        "tornado": "critical",
        "tornado.application": "error",
    }
    base_config = _find_logging_config(config)
    loggers.update(base_config.get("logging", {}))
    handler = logging.StreamHandler(sys.stderr)
    handler.setFormatter(
        logging.Formatter(
            dask.config.get("distributed.admin.log-format", config=config)
        )
    )
    logging_names = _logging_get_level_names_mapping()
    for name, raw_level in sorted(loggers.items()):
        level = (
            logging_names[raw_level.upper()]
            if isinstance(raw_level, str)
            else raw_level
        )
        logger = logging.getLogger(name)
        logger.setLevel(level)
        # Ensure that we're not registering the logger twice in this hierarchy.
        anc = logging.getLogger(None)
        already_registered = False
        for ancestor in name.split("."):
            if anc.handlers:
                already_registered = True
                break
            anc.getChild(ancestor)
        if not already_registered:
            logger.addHandler(handler)
            logger.propagate = False